Category Theory
Explore objects and maps; universal constructions; representability and algebra. Concepts and connections are available independently of video coverage.
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Products and coproducts
Products receive universal compatible maps; coproducts reverse the direction.
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Limits and colimits
Limits and colimits generalize universal constructions over diagrams of objects and arrows.
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.
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
- Universal properties · Related · Map context
- Limits and colimits · Related · Map context