If I had to describe myself using an object, I would choose a kaleidoscope. Like a kaleidoscope, I see beauty in the small, everyday things and find joy in simple pleasures. I am also able to look at situations from different perspectives, gaining new insights as the lens is turned. While my outward appearance may seem plain at first glance, looking deeper reveals vivid and ever-changing colors, patterns and possibilities. I strive to appreciate life's diversity and complexity, just as each turn of the kaleidoscope unveils fresh combinations and surprises.
The document discusses objects and classes in object-oriented programming. It defines objects as entities that represent real-world things and interact with each other, and classes as templates that define common properties and behaviors of objects. Classes are used to create multiple similar objects, and allow data and functions to be encapsulated together and hidden from external use. An example program demonstrates how a class is defined and then an object is created from the class to call member functions.
This document outlines the key functions of articles as parts of speech. It discusses the general characteristics of articles and defines the indefinite and definite articles. It then examines the functions of each type of article in detail over several paragraphs. The indefinite article can classify, indefinitize, introduce new concepts, and quantify. The definite article can identify objects, definitize objects within a context or frame, and individualize objects. The zero article performs similarly to the indefinite article but is used with uncountable nouns and plural countable nouns.
Algebraic topology uses algebra to study topological spaces. It translates questions about spaces into equivalent algebraic questions that are often easier to answer. For example, it uses the fundamental group to distinguish between a sphere and donut by showing they have different fundamental groups. Modern algebraic topology generalizes the concept of a topological space to spectra, which allows consideration of "negative-dimensional space" analogous to negative numbers extending integers.
Hand Rolled Applicative User ValidationCode KataPhilip Schwarz
Could you use a simple piece of Scala validation code (granted, a very simplistic one too!) that you can rewrite, now and again, to refresh your basic understanding of Applicative operators <*>, <*, *>?
The goal is not to write perfect code showcasing validation, but rather, to provide a small, rough-and ready exercise to reinforce your muscle-memory.
Despite its grandiose-sounding title, this deck consists of just three slides showing the Scala 3 code to be rewritten whenever the details of the operators begin to fade away.
The code is my rough and ready translation of a Haskell user-validation program found in a book called Finding Success (and Failure) in Haskell - Fall in love with applicative functors.
Direct Style Effect Systems -The Print[A] Example- A Comprehension AidPhilip Schwarz
The subject of this deck is the small Print[A] program in the following blog post by Noel Welsh: https://www.inner-product.com/posts/direct-style-effects/.
Keywords: "direct-style", "context function", "context functions", "algebraic effect", "algebraic effects", "scala", "effect system", "effect systems", "effect", "side effect", "composition", "fp", "functional programming"
Folding Cheat Sheet #4 - fourth in a seriesPhilip Schwarz
For functions that can be defined both as an instance of a right fold and as an instance of a left fold, one may be more efficient than the other.
Let's look at the example of a function 'decimal' that converts a list of digits into the corresponding decimal number.
Erratum: it has been pointed out that it is possible to define the zip function using a right fold (see slide 5).
If I had to describe myself using an object, I would choose a kaleidoscope. Like a kaleidoscope, I see beauty in the small, everyday things and find joy in simple pleasures. I am also able to look at situations from different perspectives, gaining new insights as the lens is turned. While my outward appearance may seem plain at first glance, looking deeper reveals vivid and ever-changing colors, patterns and possibilities. I strive to appreciate life's diversity and complexity, just as each turn of the kaleidoscope unveils fresh combinations and surprises.
The document discusses objects and classes in object-oriented programming. It defines objects as entities that represent real-world things and interact with each other, and classes as templates that define common properties and behaviors of objects. Classes are used to create multiple similar objects, and allow data and functions to be encapsulated together and hidden from external use. An example program demonstrates how a class is defined and then an object is created from the class to call member functions.
This document outlines the key functions of articles as parts of speech. It discusses the general characteristics of articles and defines the indefinite and definite articles. It then examines the functions of each type of article in detail over several paragraphs. The indefinite article can classify, indefinitize, introduce new concepts, and quantify. The definite article can identify objects, definitize objects within a context or frame, and individualize objects. The zero article performs similarly to the indefinite article but is used with uncountable nouns and plural countable nouns.
Algebraic topology uses algebra to study topological spaces. It translates questions about spaces into equivalent algebraic questions that are often easier to answer. For example, it uses the fundamental group to distinguish between a sphere and donut by showing they have different fundamental groups. Modern algebraic topology generalizes the concept of a topological space to spectra, which allows consideration of "negative-dimensional space" analogous to negative numbers extending integers.
Hand Rolled Applicative User ValidationCode KataPhilip Schwarz
Could you use a simple piece of Scala validation code (granted, a very simplistic one too!) that you can rewrite, now and again, to refresh your basic understanding of Applicative operators <*>, <*, *>?
The goal is not to write perfect code showcasing validation, but rather, to provide a small, rough-and ready exercise to reinforce your muscle-memory.
Despite its grandiose-sounding title, this deck consists of just three slides showing the Scala 3 code to be rewritten whenever the details of the operators begin to fade away.
The code is my rough and ready translation of a Haskell user-validation program found in a book called Finding Success (and Failure) in Haskell - Fall in love with applicative functors.
Direct Style Effect Systems -The Print[A] Example- A Comprehension AidPhilip Schwarz
The subject of this deck is the small Print[A] program in the following blog post by Noel Welsh: https://www.inner-product.com/posts/direct-style-effects/.
Keywords: "direct-style", "context function", "context functions", "algebraic effect", "algebraic effects", "scala", "effect system", "effect systems", "effect", "side effect", "composition", "fp", "functional programming"
Folding Cheat Sheet #4 - fourth in a seriesPhilip Schwarz
For functions that can be defined both as an instance of a right fold and as an instance of a left fold, one may be more efficient than the other.
Let's look at the example of a function 'decimal' that converts a list of digits into the corresponding decimal number.
Erratum: it has been pointed out that it is possible to define the zip function using a right fold (see slide 5).
Folding Cheat Sheet #3 - third in a seriesPhilip Schwarz
This document summarizes the universal property of fold, which states that for finite lists the fold function is the unique function that satisfies its defining recursive equations. It provides examples of how common list functions like sum, product, length, concatenation (⧺) can be defined in terms of fold. It also notes that the universal property can be generalized to handle partial and infinite lists. Finally, it states that map, filter and fold form the "triad" or basic building blocks of functional programming.
Folding Cheat Sheet #2 - second in a seriesPhilip Schwarz
This document provides definitions and examples of foldr and foldl functions in functional programming. Foldr recursively applies a function from right to left, associating at each step. Foldl recursively applies a function from left to right, associating at each step. Examples are given applying foldr and foldl to a list with elements a0 through a3, using a function f and initial value b. Programmatic and mathematical definitions of foldr and foldl are also presented.
Folding Cheat Sheet #1 - first in a seriesPhilip Schwarz
This document provides examples of using fold functions to define recursive functions over natural numbers (Nat) and lists. It shows common patterns for defining recursive functions over Nat using foldn and over lists using foldr. Three examples are given of functions defined over Nat using foldn: addition, multiplication, and exponentiation. Three examples are also given of functions defined over lists using foldr: sum, length, and append.
Tagless Final Encoding - Algebras and Interpreters and also ProgramsPhilip Schwarz
Tagless Final Encoding - Algebras and Interpreters and also Programs - An introduction, through the work of Gabriel Volpe.
Slide deck home: http://fpilluminated.com/assets/tagless-final-encoding-algebras-interpreters-and-programs.html
A sighting of traverseFilter and foldMap in Practical FP in ScalaPhilip Schwarz
Slide deck home: http://fpilluminated.com/assets/sighting-of-scala-cats-traverseFilter-and-foldMap-in-practical-fp-in-scala.html.
Download PDF for perfect image quality.
A sighting of sequence function in Practical FP in ScalaPhilip Schwarz
Slide deck home: http://fpilluminated.com/assets/sighting-of-scala-cats-sequence-function-in-practical-fp-in-scala.html.
Download PDF for perfect image quality.
This talk was presented on Aug 3rd 2023 during the Scala in the City event a ITV in London https://www.meetup.com/scala-in-the-city/events/292844968/
Visit the following for a description, slideshow, all slides with transcript, pdf, github repo, and eventually a video recording: http://fpilluminated.com/assets/n-queens-combinatorial-puzzle-meets-cats.html
At the centre of this talk is the N-Queens combinatorial puzzle. The reason why this puzzle features in the Scala book and functional programming course by Martin Odersky (the language’s creator), is that such puzzles are a particularly suitable application area of 'for comprehensions'.
We’ll start by (re)acquainting ourselves with the puzzle, and seeing the role played in it by permutations. Next, we’ll see how, when wanting to visualise candidate puzzle solutions, Cats’ monoidal functions fold and foldMap are a great fit for combining images.
While we are all very familiar with the triad providing the bread, butter and jam of functional programming, i.e. map, filter and fold, not everyone knows about the corresponding functions in Cats’ monadic variant of the triad, i.e. mapM, filterM and foldM, which we are going to learn about next.
As is often the case in functional programming, the traverse function makes an appearance, and we shall grab the opportunity to point out the symmetry that exists in the interrelation of flatMap / foldMap / traverse and flatten / fold / sequence.
Armed with an understanding of foldM, we then look at how such a function can be used to implement an iterative algorithm for the N-Queens puzzle.
The talk ends by pointing out that the iterative algorithm is smarter than the recursive one, because it ‘remembers’ where it has already placed previous queens.
Kleisli composition, flatMap, join, map, unit - implementation and interrelat...Philip Schwarz
Kleisli composition, flatMap, join, map, unit. A study/memory aid, to help learn/recall their implementation/interrelation.
Version 2, updated for Scala 3
Nat, List and Option Monoids -from scratch -Combining and Folding -an examplePhilip Schwarz
Nat, List and Option Monoids, from scratch. Combining and Folding: an example.
This is a new version of the original which has some cosmetic changes and a new 7th slide which only differs from slide 6 in that it defines the fold function in terms of the foldRight function.
Code: https://github.com/philipschwarz/nat-list-and-option-monoids-from-scratch-combining-and-folding-an-example
Nat, List and Option Monoids -from scratch -Combining and Folding -an examplePhilip Schwarz
Nat, List and Option Monoids, from scratch. Combining and Folding: an example.
Code: https://github.com/philipschwarz/nat-list-and-option-monoids-from-scratch-combining-and-folding-an-example
The Sieve of Eratosthenes - Part II - Genuine versus Unfaithful Sieve - Haske...Philip Schwarz
When I posted the deck for Part 1 to the Scala users forum, Odd Möller linked to a paper titled "The Genuine Sieve of Eratosthenes", which speaks of the Unfaithful Sieve.
Part 2 is based on that paper and on Richard Bird's faithful Haskell implementation of the Sieve, which we translate into Scala.
Scala code for Richard Bird's infinite primes Haskell program: https://github.com/philipschwarz/sieve-of-eratosthenes-part-2-scala
Sum and Product Types -The Fruit Salad & Fruit Snack Example - From F# to Ha...Philip Schwarz
- The document describes how product types (built using AND) and sum types (built using OR) are used to define types for representing fruit salads and fruit snacks in F#, Haskell, Scala, and Java.
- Product types combine elements and are used to define the FruitSalad type, while sum types allow alternatives and are used to define the FruitSnack type consisting of different fruits.
- Pattern matching is demonstrated to write functions that analyze and return different strings based on the values of FruitSalad and FruitSnack types.
Jordan Peterson - The pursuit of meaning and related ethical axiomsPhilip Schwarz
I have only recently become aware of the work of Jordan Peterson. Because I am finding it so interesting, I hope that the following small collection of excerpts from some of his writings and speeches might entice any fellow latecomers to find out more about his work. See below for my own summary of some of the subjects touched upon in these slides.
Download for best results.
Defining filter using (a) recursion (b) folding (c) folding with S, B and I c...Philip Schwarz
Defining filter using
(a) recursion
(b) folding
(c) folding with S, B and I combinators
(d) folding with applicative functor and identity function.pdf
This second version adds a simpler folding definition, which I had left out in the first version.
WWDC 2024 Keynote Review: For CocoaCoders AustinPatrick Weigel
Overview of WWDC 2024 Keynote Address.
Covers: Apple Intelligence, iOS18, macOS Sequoia, iPadOS, watchOS, visionOS, and Apple TV+.
Understandable dialogue on Apple TV+
On-device app controlling AI.
Access to ChatGPT with a guest appearance by Chief Data Thief Sam Altman!
App Locking! iPhone Mirroring! And a Calculator!!
UI5con 2024 - Boost Your Development Experience with UI5 Tooling ExtensionsPeter Muessig
The UI5 tooling is the development and build tooling of UI5. It is built in a modular and extensible way so that it can be easily extended by your needs. This session will showcase various tooling extensions which can boost your development experience by far so that you can really work offline, transpile your code in your project to use even newer versions of EcmaScript (than 2022 which is supported right now by the UI5 tooling), consume any npm package of your choice in your project, using different kind of proxies, and even stitching UI5 projects during development together to mimic your target environment.
Folding Cheat Sheet #3 - third in a seriesPhilip Schwarz
This document summarizes the universal property of fold, which states that for finite lists the fold function is the unique function that satisfies its defining recursive equations. It provides examples of how common list functions like sum, product, length, concatenation (⧺) can be defined in terms of fold. It also notes that the universal property can be generalized to handle partial and infinite lists. Finally, it states that map, filter and fold form the "triad" or basic building blocks of functional programming.
Folding Cheat Sheet #2 - second in a seriesPhilip Schwarz
This document provides definitions and examples of foldr and foldl functions in functional programming. Foldr recursively applies a function from right to left, associating at each step. Foldl recursively applies a function from left to right, associating at each step. Examples are given applying foldr and foldl to a list with elements a0 through a3, using a function f and initial value b. Programmatic and mathematical definitions of foldr and foldl are also presented.
Folding Cheat Sheet #1 - first in a seriesPhilip Schwarz
This document provides examples of using fold functions to define recursive functions over natural numbers (Nat) and lists. It shows common patterns for defining recursive functions over Nat using foldn and over lists using foldr. Three examples are given of functions defined over Nat using foldn: addition, multiplication, and exponentiation. Three examples are also given of functions defined over lists using foldr: sum, length, and append.
Tagless Final Encoding - Algebras and Interpreters and also ProgramsPhilip Schwarz
Tagless Final Encoding - Algebras and Interpreters and also Programs - An introduction, through the work of Gabriel Volpe.
Slide deck home: http://fpilluminated.com/assets/tagless-final-encoding-algebras-interpreters-and-programs.html
A sighting of traverseFilter and foldMap in Practical FP in ScalaPhilip Schwarz
Slide deck home: http://fpilluminated.com/assets/sighting-of-scala-cats-traverseFilter-and-foldMap-in-practical-fp-in-scala.html.
Download PDF for perfect image quality.
A sighting of sequence function in Practical FP in ScalaPhilip Schwarz
Slide deck home: http://fpilluminated.com/assets/sighting-of-scala-cats-sequence-function-in-practical-fp-in-scala.html.
Download PDF for perfect image quality.
This talk was presented on Aug 3rd 2023 during the Scala in the City event a ITV in London https://www.meetup.com/scala-in-the-city/events/292844968/
Visit the following for a description, slideshow, all slides with transcript, pdf, github repo, and eventually a video recording: http://fpilluminated.com/assets/n-queens-combinatorial-puzzle-meets-cats.html
At the centre of this talk is the N-Queens combinatorial puzzle. The reason why this puzzle features in the Scala book and functional programming course by Martin Odersky (the language’s creator), is that such puzzles are a particularly suitable application area of 'for comprehensions'.
We’ll start by (re)acquainting ourselves with the puzzle, and seeing the role played in it by permutations. Next, we’ll see how, when wanting to visualise candidate puzzle solutions, Cats’ monoidal functions fold and foldMap are a great fit for combining images.
While we are all very familiar with the triad providing the bread, butter and jam of functional programming, i.e. map, filter and fold, not everyone knows about the corresponding functions in Cats’ monadic variant of the triad, i.e. mapM, filterM and foldM, which we are going to learn about next.
As is often the case in functional programming, the traverse function makes an appearance, and we shall grab the opportunity to point out the symmetry that exists in the interrelation of flatMap / foldMap / traverse and flatten / fold / sequence.
Armed with an understanding of foldM, we then look at how such a function can be used to implement an iterative algorithm for the N-Queens puzzle.
The talk ends by pointing out that the iterative algorithm is smarter than the recursive one, because it ‘remembers’ where it has already placed previous queens.
Kleisli composition, flatMap, join, map, unit - implementation and interrelat...Philip Schwarz
Kleisli composition, flatMap, join, map, unit. A study/memory aid, to help learn/recall their implementation/interrelation.
Version 2, updated for Scala 3
Nat, List and Option Monoids -from scratch -Combining and Folding -an examplePhilip Schwarz
Nat, List and Option Monoids, from scratch. Combining and Folding: an example.
This is a new version of the original which has some cosmetic changes and a new 7th slide which only differs from slide 6 in that it defines the fold function in terms of the foldRight function.
Code: https://github.com/philipschwarz/nat-list-and-option-monoids-from-scratch-combining-and-folding-an-example
Nat, List and Option Monoids -from scratch -Combining and Folding -an examplePhilip Schwarz
Nat, List and Option Monoids, from scratch. Combining and Folding: an example.
Code: https://github.com/philipschwarz/nat-list-and-option-monoids-from-scratch-combining-and-folding-an-example
The Sieve of Eratosthenes - Part II - Genuine versus Unfaithful Sieve - Haske...Philip Schwarz
When I posted the deck for Part 1 to the Scala users forum, Odd Möller linked to a paper titled "The Genuine Sieve of Eratosthenes", which speaks of the Unfaithful Sieve.
Part 2 is based on that paper and on Richard Bird's faithful Haskell implementation of the Sieve, which we translate into Scala.
Scala code for Richard Bird's infinite primes Haskell program: https://github.com/philipschwarz/sieve-of-eratosthenes-part-2-scala
Sum and Product Types -The Fruit Salad & Fruit Snack Example - From F# to Ha...Philip Schwarz
- The document describes how product types (built using AND) and sum types (built using OR) are used to define types for representing fruit salads and fruit snacks in F#, Haskell, Scala, and Java.
- Product types combine elements and are used to define the FruitSalad type, while sum types allow alternatives and are used to define the FruitSnack type consisting of different fruits.
- Pattern matching is demonstrated to write functions that analyze and return different strings based on the values of FruitSalad and FruitSnack types.
Jordan Peterson - The pursuit of meaning and related ethical axiomsPhilip Schwarz
I have only recently become aware of the work of Jordan Peterson. Because I am finding it so interesting, I hope that the following small collection of excerpts from some of his writings and speeches might entice any fellow latecomers to find out more about his work. See below for my own summary of some of the subjects touched upon in these slides.
Download for best results.
Defining filter using (a) recursion (b) folding (c) folding with S, B and I c...Philip Schwarz
Defining filter using
(a) recursion
(b) folding
(c) folding with S, B and I combinators
(d) folding with applicative functor and identity function.pdf
This second version adds a simpler folding definition, which I had left out in the first version.
WWDC 2024 Keynote Review: For CocoaCoders AustinPatrick Weigel
Overview of WWDC 2024 Keynote Address.
Covers: Apple Intelligence, iOS18, macOS Sequoia, iPadOS, watchOS, visionOS, and Apple TV+.
Understandable dialogue on Apple TV+
On-device app controlling AI.
Access to ChatGPT with a guest appearance by Chief Data Thief Sam Altman!
App Locking! iPhone Mirroring! And a Calculator!!
UI5con 2024 - Boost Your Development Experience with UI5 Tooling ExtensionsPeter Muessig
The UI5 tooling is the development and build tooling of UI5. It is built in a modular and extensible way so that it can be easily extended by your needs. This session will showcase various tooling extensions which can boost your development experience by far so that you can really work offline, transpile your code in your project to use even newer versions of EcmaScript (than 2022 which is supported right now by the UI5 tooling), consume any npm package of your choice in your project, using different kind of proxies, and even stitching UI5 projects during development together to mimic your target environment.
UI5con 2024 - Bring Your Own Design SystemPeter Muessig
How do you combine the OpenUI5/SAPUI5 programming model with a design system that makes its controls available as Web Components? Since OpenUI5/SAPUI5 1.120, the framework supports the integration of any Web Components. This makes it possible, for example, to natively embed own Web Components of your design system which are created with Stencil. The integration embeds the Web Components in a way that they can be used naturally in XMLViews, like with standard UI5 controls, and can be bound with data binding. Learn how you can also make use of the Web Components base class in OpenUI5/SAPUI5 to also integrate your Web Components and get inspired by the solution to generate a custom UI5 library providing the Web Components control wrappers for the native ones.
Top Benefits of Using Salesforce Healthcare CRM for Patient Management.pdfVALiNTRY360
Salesforce Healthcare CRM, implemented by VALiNTRY360, revolutionizes patient management by enhancing patient engagement, streamlining administrative processes, and improving care coordination. Its advanced analytics, robust security, and seamless integration with telehealth services ensure that healthcare providers can deliver personalized, efficient, and secure patient care. By automating routine tasks and providing actionable insights, Salesforce Healthcare CRM enables healthcare providers to focus on delivering high-quality care, leading to better patient outcomes and higher satisfaction. VALiNTRY360's expertise ensures a tailored solution that meets the unique needs of any healthcare practice, from small clinics to large hospital systems.
For more info visit us https://valintry360.com/solutions/health-life-sciences
SOCRadar's Aviation Industry Q1 Incident Report is out now!
The aviation industry has always been a prime target for cybercriminals due to its critical infrastructure and high stakes. In the first quarter of 2024, the sector faced an alarming surge in cybersecurity threats, revealing its vulnerabilities and the relentless sophistication of cyber attackers.
SOCRadar’s Aviation Industry, Quarterly Incident Report, provides an in-depth analysis of these threats, detected and examined through our extensive monitoring of hacker forums, Telegram channels, and dark web platforms.
Mobile App Development Company In Noida | Drona InfotechDrona Infotech
Drona Infotech is a premier mobile app development company in Noida, providing cutting-edge solutions for businesses.
Visit Us For : https://www.dronainfotech.com/mobile-application-development/
When it is all about ERP solutions, companies typically meet their needs with common ERP solutions like SAP, Oracle, and Microsoft Dynamics. These big players have demonstrated that ERP systems can be either simple or highly comprehensive. This remains true today, but there are new factors to consider, including a promising new contender in the market that’s Odoo. This blog compares Odoo ERP with traditional ERP systems and explains why many companies now see Odoo ERP as the best choice.
What are ERP Systems?
An ERP, or Enterprise Resource Planning, system provides your company with valuable information to help you make better decisions and boost your ROI. You should choose an ERP system based on your company’s specific needs. For instance, if you run a manufacturing or retail business, you will need an ERP system that efficiently manages inventory. A consulting firm, on the other hand, would benefit from an ERP system that enhances daily operations. Similarly, eCommerce stores would select an ERP system tailored to their needs.
Because different businesses have different requirements, ERP system functionalities can vary. Among the various ERP systems available, Odoo ERP is considered one of the best in the ERp market with more than 12 million global users today.
Odoo is an open-source ERP system initially designed for small to medium-sized businesses but now suitable for a wide range of companies. Odoo offers a scalable and configurable point-of-sale management solution and allows you to create customised modules for specific industries. Odoo is gaining more popularity because it is built in a way that allows easy customisation, has a user-friendly interface, and is affordable. Here, you will cover the main differences and get to know why Odoo is gaining attention despite the many other ERP systems available in the market.
Mobile app Development Services | Drona InfotechDrona Infotech
Drona Infotech is one of the Best Mobile App Development Company In Noida Maintenance and ongoing support. mobile app development Services can help you maintain and support your app after it has been launched. This includes fixing bugs, adding new features, and keeping your app up-to-date with the latest
Visit Us For :
What to do when you have a perfect model for your software but you are constrained by an imperfect business model?
This talk explores the challenges of bringing modelling rigour to the business and strategy levels, and talking to your non-technical counterparts in the process.
Malibou Pitch Deck For Its €3M Seed Roundsjcobrien
French start-up Malibou raised a €3 million Seed Round to develop its payroll and human resources
management platform for VSEs and SMEs. The financing round was led by investors Breega, Y Combinator, and FCVC.
Most important New features of Oracle 23c for DBAs and Developers. You can get more idea from my youtube channel video from https://youtu.be/XvL5WtaC20A
Microservice Teams - How the cloud changes the way we workSven Peters
A lot of technical challenges and complexity come with building a cloud-native and distributed architecture. The way we develop backend software has fundamentally changed in the last ten years. Managing a microservices architecture demands a lot of us to ensure observability and operational resiliency. But did you also change the way you run your development teams?
Sven will talk about Atlassian’s journey from a monolith to a multi-tenanted architecture and how it affected the way the engineering teams work. You will learn how we shifted to service ownership, moved to more autonomous teams (and its challenges), and established platform and enablement teams.
1. Let’s talk about how monoids map onto category theory.
I could say “any category with a single object is a monoid”
and then just walk off stage, which is what some people did
to me when I was first learning category theory, but I think
the actual explanation is more interesting and enlightening.
If you think about integers, the integers with addition and
zero as identity, and then we think about what my definition
of category was, there is nothing in that definiton that said I
can’t have multiple arrows starting and ending at a given
object.
So we’ll have one object and we’ll
just have a bunch of arrows starting
and ending at that object. And think
of these arrows not at functions but
as each element of the monoid set.
So in the case of integers, think of x
and y as 1 or as 2 or as 3 etc, as
actual integers. And categories
require that given any two arrows
where the domain and codomain
match, we should be able to form
their composition.
So the composition between two
arrows here is going to be this
monoid composition that we
talked about before.
And then similarly, the category is
going to require for every object,
in this case a single object, to have
an identity arrow, such that it is
going to be a left and right identity
with respect to arrow
composition.
That’s just going to be the monoid identity that we talked
about earlier. So in categorical language, this identity
composed with x should be the same as x, and the way we
have defined composition here is going to be the monoid
composition and hopefully we can see that the category
laws map onto the Monoid laws appropriately.
Here I started with an existing monoid, and then sort of
shown how that translates to categories, but we can also
take a category of one object and map that back to a Monoid
because the requirements for being a category are going to
be the same as the requirements for being a monoid. @adelbertchang
Simplicity in Composition
Adelbert Chang explains how monoids
map onto category theory
Category Theory
Monoid
1
2
3
4 5
6
monoid
composition
arrow
composition
identity arrow
monoid
identity