Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Categorical isomorphisms
A morphism is an isomorphism when it has a two-sided compositional inverse.
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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.
Equivalence of categories
Functors inverse up to natural isomorphism express equivalence without literal equality of categories.
Knowledge connections
- Natural transformations · Related · Map context
- Categories · Related · Map context