Category Theory for Programmers

Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.

That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.

Table of contents

Category: The Essence of Composition
Types and Functions
Categories Great and Small
Kleisli Categories
Products and Coproducts
Simple Algebraic Data Types
Functors
Functoriality
Function Types
Natural Transformations
Declarative Programming
Limits and Colimits
Free Monoids
Representable Functors
The Yoneda Lemma
Yoneda Embedding
It's All About Morphisms
Adjunctions
Free/Forgetful Adjunctions
Monads: Programmer's Definition
Monads and Effects
Monads Categorically
Comonads
F-Algebras
Algebras for Monads
Ends and Coends
Kan Extensions
Enriched Categories
Topoi
Lawvere Theories
Monads, Monoids, and Categories

Pages :	498
Size :	16.3 MB
Downloads:	66
Created:	2022-02-01
License:	CC BY-SA
Author(s):	by Bartosz Milewski

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