Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Equivalence of categories
Functors inverse up to natural isomorphism express equivalence without literal equality of categories.
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Monoidal categories
A tensor-like product and unit object obey coherent associativity and unit constraints.
Yoneda lemma
Maps from a representable functor into a functor correspond naturally to an element at its representing object.
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
- Yoneda lemma · Related · Map context
- Monoidal categories · Related · Map context