Fri Jan 19
The "opposite category" is a functor Cat -> Cat.
The functors Hom(X,*) : C -> Set and Hom(*,X) : Cop -> Set.
Natural isomorphisms.
The product of two categories.
Given functors C->D or D->C, we get functors Cop x D -> Set.
If they're naturally isomorphic, call the functors adjoint.
Left adjoints of several forgetful functors. The right adjoint of forget : Top -> Set.
The functors Hom(X,*) : C -> Set and Hom(*,X) : Cop -> Set.
Natural isomorphisms.
The product of two categories.
Given functors C->D or D->C, we get functors Cop x D -> Set.
If they're naturally isomorphic, call the functors adjoint.
Left adjoints of several forgetful functors. The right adjoint of forget : Top -> Set.
posted by Allen Knutson @ 2:10 PM
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