# Category Theory * Category theory * [Category theory](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/category-theory) * [Category](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/category) * [Category object](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/category-object.md) * [Arrow](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/arrow.md) * [Ordered category](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/ordered-category.md) * [Concrete category](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/concrete-category.md) * [Initial Object](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/initial-object) * [Terminal Object](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/terminal-object) * [Duals](https://mandober.gitbook.io/math-debrief/450-category-theory/broken-reference) * [Product](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/product) * [Coproduct](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/coproduct) * [Universal construction](https://mandober.gitbook.io/math-debrief/450-category-theory/07-constructions/universal-construction) * [Kleisi category](https://mandober.gitbook.io/math-debrief/450-category-theory/10-categories/kleisi-category) * [Functor](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/functor.md) * [Natural transformation](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/natural-transformation) * [Monad](https://mandober.gitbook.io/math-debrief/450-category-theory/broken-reference) ## Category Theory by Bartosz Milewski Part One * [Category](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/category): The Essence of Composition * Types and Functions * Categories Great and Small * [Category](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/category) * [Arrow](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/arrow.md) * [Ordered category](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/ordered-category.md) * [Kleisli Categories](https://mandober.gitbook.io/math-debrief/450-category-theory/10-categories/kleisi-category) * [Products](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/product) * [Coproducts](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/coproduct) * [Algebraic Data Types](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/algebraic-data-types) * [Functors](https://github.com/mandober/debrief.math/tree/1303f9c4d1763e93618e71cea4b00554bb65a514/450-category-theory/terms/functor.md) * [Functoriality](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/functoriality) * Bifunctors * Profunctors * Contravariant * [Function Types](https://mandober.gitbook.io/math-debrief/450-category-theory/terms/function-type) * 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](https://bartoszmilewski.com/2014/11/04/category-the-essence-of-composition/) * [Types and Functions](https://bartoszmilewski.com/2014/11/24/types-and-functions/) * [Categories Great and Small](https://bartoszmilewski.com/2014/12/05/categories-great-and-small/) * [Kleisli Categories](https://bartoszmilewski.com/2014/12/23/kleisli-categories/) * [Products and Coproducts](https://bartoszmilewski.com/2015/01/07/products-and-coproducts/) * [Simple Algebraic Data Types](https://bartoszmilewski.com/2015/01/13/simple-algebraic-data-types/) * [Functors](https://bartoszmilewski.com/2015/01/20/functors/) * [Functoriality](https://bartoszmilewski.com/2015/02/03/functoriality/) * [Function Types](https://bartoszmilewski.com/2015/03/13/function-types/) * [Natural Transformations](https://bartoszmilewski.com/2015/04/07/natural-transformations/) Part Two * [Declarative Programming](https://bartoszmilewski.com/2015/04/15/category-theory-and-declarative-programming/) * [Limits and Colimits](https://bartoszmilewski.com/2015/04/15/limits-and-colimits/) * [Free Monoids](https://bartoszmilewski.com/2015/07/21/free-monoids/) * [Representable Functors](https://bartoszmilewski.com/2015/07/29/representable-functors/) * [The Yoneda Lemma](https://bartoszmilewski.com/2015/09/01/the-yoneda-lemma/) * [Yoneda Embedding](https://bartoszmilewski.com/2015/10/28/yoneda-embedding/) Part Three * [It's All About Morphisms](https://bartoszmilewski.com/2015/11/17/its-all-about-morphisms/) * [Adjunctions](https://bartoszmilewski.com/2016/04/18/adjunctions/) * [Free/Forgetful Adjunctions](https://bartoszmilewski.com/2016/06/15/freeforgetful-adjunctions/) * [Monads: Programmer's Definition](https://bartoszmilewski.com/2016/11/21/monads-programmers-definition/) * [Monads and Effects](https://bartoszmilewski.com/2016/11/30/monads-and-effects/) * [Monads Categorically](https://bartoszmilewski.com/2016/12/27/monads-categorically/) * [Comonads](https://bartoszmilewski.com/2017/01/02/comonads/) * [F-Algebras](https://bartoszmilewski.com/2017/02/28/f-algebras/) * [Algebras for Monads](https://bartoszmilewski.com/2017/03/14/algebras-for-monads/) * [Ends and Coends](https://bartoszmilewski.com/2017/03/29/ends-and-coends/) * [Kan Extensions](https://bartoszmilewski.com/2017/04/17/kan-extensions/) * [Enriched Categories](https://bartoszmilewski.com/2017/05/13/enriched-categories/) * [Topoi](https://bartoszmilewski.com/2017/07/22/topoi/) * [Lawvere Theories](https://bartoszmilewski.com/2017/08/26/lawvere-theories/) * [Monads, Monoids, and Categories](https://bartoszmilewski.com/2017/09/06/monads-monoids-and-categories/) PDF version * [pdf version](https://github.com/hmemcpy/milewski-ctfp-pdf/)