Base Definitions Category Theory by Example
Objects, morphisms, composition, identity morphisms, categories, and the category of sets provide the base language for the series.
Topic
category theory
Curry-Howard-Lambek Correspondence Category Theory by Example
The Curry-Howard-Lambek correspondence relates propositions, proofs, programs, and categorical structure.
Limits Category Theory by Example
Limits and colimits express universal constructions through cones, cocones, terminal objects, products, sums, and equalizers.
Monads Category Theory by Example
Monads arise from monoids in the category of endofunctors and model structured computation in programming languages.
Objects and Morphisms Category Theory by Example
Universal constructions describe initial and terminal objects, products, sums, monoids, exponential objects, and type algebra.
Introduction Category Theory by Example
The series introduces category theory as a connected collection of definitions, examples, and applications in sets, programming languages, and physics.
Abstract Algebra Category Theory by Example
Groups, rings, fields, and vector spaces provide algebraic background used by the categorical examples.
Topos Category Theory by Example
Topos theory studies categories that behave like generalized universes of sets.
Yoneda's Lemma Category Theory by Example
Yoneda's lemma explains how an object of a locally small category is determined by the morphisms into or out of it.
Natural Transformations Category Theory by Example
Natural transformations compare functors component by component and organize functors into their own categories.
Functors Category Theory by Example
Functors map objects and morphisms between categories while preserving composition and identity.
Kleisli Category Category Theory by Example
Kleisli categories describe composition for computations with effects such as partiality, exceptions, and nondeterminism.