Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Categories
A category has objects, morphisms, associative composition and identity morphisms.
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Categorical isomorphisms
A morphism is an isomorphism when it has a two-sided compositional inverse.
Function composition
Composition applies one function after another where the output fits the next domain.
Functors
A functor maps objects and morphisms while preserving identities and composition.
Universal properties
A universal property characterizes an object by unique compatible maps.
Abelian categories
An abelian category supports additive structure, kernels, cokernels and exactness with compatible axioms.
Knowledge connections
- Functors · Related · Map context
- Categorical isomorphisms · Related · Map context
- Function composition · Related · Map context
- Universal properties · Related · Map context
- Functors · Next concept · Map context
- Function composition · Prerequisite · Map context