Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Monoidal categories
A tensor-like product and unit object obey coherent associativity and unit constraints.
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Abelian categories
An abelian category supports additive structure, kernels, cokernels and exactness with compatible axioms.
Equivalence of categories
Functors inverse up to natural isomorphism express equivalence without literal equality of categories.
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.
Categories
A category has objects, morphisms, associative composition and identity morphisms.
Knowledge connections
- Equivalence of categories · Related · Map context
- Abelian categories · Related · Map context