Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
FOLLOW AN IDEA
Functors
A functor maps objects and morphisms while preserving identities and composition.
Explore concept graph · Explore connected videos
Different ways to understand it
No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video
More concepts to explore
Categories
A category has objects, morphisms, associative composition and identity morphisms.
Natural transformations
Compatible morphisms between functor values commute with every source-category morphism.
Abelian categories
An abelian category supports additive structure, kernels, cokernels and exactness with compatible axioms.
Adjunctions
An adjunction relates morphism sets naturally between two functors.
Categorical isomorphisms
A morphism is an isomorphism when it has a two-sided compositional inverse.
Knowledge connections
- Categories · Related · Map context
- Natural transformations · Related · Map context
- Categories · Prerequisite · Map context
- Natural transformations · Next concept · Map context