category theory

category

functor

natural transformation

Cat

universal construction

representable functor

adjoint functor

limit/colimit

weighted limit

end/coend

Kan extension

Yoneda lemma

Isbell duality

Grothendieck construction

adjoint functor theorem

monadicity theorem

adjoint lifting theorem

Tannaka duality

Gabriel-Ulmer duality

small object argument

Freyd-Mitchell embedding theorem

relation between type theory and category theory

sheaf and topos theory

enriched category theory

higher category theory

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An umbrella category is an inhabited category $C$ such that for every object $X$ in $C$, there is at least one subterminal object $T$ such that the hom-set $C(X,T)$ is inhabited (hence being a singleton).

Created on June 26, 2011 at 15:54:31. See the history of this page for a list of all contributions to it.