Category Theory

• Category theory

  • Category theory

  • Category

  • Category object

  • Arrow

  • Ordered category

  • Concrete category

  • Initial Object

  • Terminal Object

  • Duals

  • Product

  • Coproduct

  • Universal construction

  • Kleisi category

  • Functor

  • Natural transformation

  • Monad

Category Theory by Bartosz Milewski

https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

Part One

• Category: The Essence of Composition

• Types and Functions

• Categories Great and Small

  • Category

  • Arrow

  • Ordered category

• Kleisli Categories

• Products

• Coproducts

• Algebraic Data Types

• Functors

• Functoriality

  • Bifunctors

  • Profunctors

  • Contravariant

• Function Types

  • Universal Construction

  • Exponentials

  • Cartesian Closed Categories

  • Exponentials and Algebraic Data Types

  • Curry-Howard Isomorphism

• Natural Transformations

Part Two

• Declarative Programming

• Limits and Colimits

• Free Monoids

• Representable Functors

• The Yoneda Lemma

• Yoneda Embedding

Part Three

• 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

Part One

• 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

Part Two

• Declarative Programming

• Limits and Colimits

• Free Monoids

• Representable Functors

• The Yoneda Lemma

• Yoneda Embedding

Part Three

• 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

PDF version

• pdf version