Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Natural transformations
Compatible morphisms between functor values commute with every source-category morphism.
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Categorical isomorphisms
A morphism is an isomorphism when it has a two-sided compositional inverse.
Functors
A functor maps objects and morphisms while preserving identities and composition.
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.
Categories
A category has objects, morphisms, associative composition and identity morphisms.
Knowledge connections
- Functors · Related · Map context
- Categorical isomorphisms · Related · Map context
- Functors · Prerequisite · Map context