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55
votes
9answers
6k views

How do I check if a functor has a (left/right) adjoint?

Because adjoint functors are just cool, and knowing that a pair of functors is an adjoint pair gives you a bunch of information from generalized abstract nonsense, I often find myself saying, "Hey, ...
27
votes
4answers
2k views

Does a scheme have a “separification”?

Background: (1) If C and D are categories and there is a forgetful functor U:C→D, then a C-ification functor F:D→C is an adjoint to U. For example, the (left) adjoint to the forgetful ...
1
vote
3answers
433 views

Another adjoint pair: Definable sets and set-builder formulas

I see adjointness between the two concepts of "being a definable set" and "being a set-builder formula": A set $X$ is definable when there is a formula $\phi(x)$ such that $X = \lbrace x : ...