Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Abelian categories
An abelian category supports additive structure, kernels, cokernels and exactness with compatible axioms.
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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.
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
- Monoidal categories · Related · Map context
- Yoneda lemma · Related · Map context