Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Universal properties
A universal property characterizes an object by unique compatible maps.
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Adjunctions
An adjunction relates morphism sets naturally between two functors.
Categories
A category has objects, morphisms, associative composition and identity morphisms.
Products and coproducts
Products receive universal compatible maps; coproducts reverse the direction.
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.
Knowledge connections
- Products and coproducts · Related · Map context
- Adjunctions · Related · Map context
- Categories · Related · Map context
- Yoneda lemma · Related · Map context