The document discusses the relevance of category theory for programmers, emphasizing its applications in data modeling and understanding Haskell. It introduces key concepts such as monoids, functors, graphs, and their relationship to database schemas, where tables represent vertices and foreign keys represent arrows. Additionally, it outlines a specific example involving employees and managers within a departmental structure.

1. CATEGORY THEORY
FOR PROGRAMMERS

2. WHY?
▸ You want to do data modelling (database)
▸ You know Haskell and want to understand it better
▸ You want to be a better programmer

9. Monoid
! id f g h
Category with one object
Multiple arrows pointing to itself

10. Functor
a
b
F a
F a
F
F
f fmap
fmap: (a → b) → (F a → F b)
C D

11. Set
domain of f
domain of g
codomain of f
codomain of g
f ○ g: X → Z

12. Commutative Diagram
A
C
B
f
g
h
DNA
Amino Acid
RNA
codes for
codes for
codes for

13. Ologs
TypeType
aspectaspect
Type
A mobile noa name
has
a person
A date of
birth
hashas
(valid aspect) (valid aspect) (invalid aspect)
Because there maybe be 0 or
multiple no’s per person, and no’s
can change too.

14. Graphs
f
A Graph G := (V, A, src, tgt)
v
u
w
g
V
u
v
w
A src tgt
f u v
g u w
V - A set of vertices
tgt - target function
A - A set of Arrows
src - source function

15. Database Schema
Name
Person
Date of
Birth
Employee
Mobile No
Manager
Vertices are tables
Arrows are foreign keys
All tables will have an
id column
Manager
is a graph with rules
Department
Rule 1 : Employees and their manager must be in the same department