adjoint functor theorem
adjoint lifting theorem
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 extremal monomorphism in a category C is a monomorphism m such that if m=ge where e is an epimorphism, then e is an isomorphism.
The dual concept is extremal epimorphism, and all properties of extremal epimorphisms apply in the dual sense to extremal monomorphisms.
In Top the extremal monomorphisms coincide with the regular monomorphisms, and these are exactly the subspace embeddings.