The adjoint-functors tag has no wiki summary.

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### bar-cobar or cobar-bar

What is the standard or best reference for the adjointnes of bar and cobar constructions?

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### Constructing pointwise Kan extensions as adjoints to some functor

Background
I'm working on formalizing some category theory in Coq at https://bitbucket.org/JasonGross/catdb. Currently, I'm in the process of formalizing pointwise Kan extensions. Partly because ...

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### Proving the Special Adjoint Functor Theorem from the general Adjoint Functor Theorem

Often, when dealing with adjoint functor theorems, people go about proving each one separately, from first principles if you will (this is the course taken in MacLane). However, the names suggest ...

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### Do generalizations of adjoint functors, such as adjunctions in 2-categories, and multivariable adjunctions, have formulations in terms of something like universal morphisms?

I recently learned about two-variable adjunctions and multi-variable adjunctions, and about adjunctions in 2-categories. The nCatLab page on two-variable adjunctions talks about how to go from the ...

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### Are the only universal (co-)universal conditions (co-)limits?

Reading this title, you may have thought there was a typo, but there isn't (well I don't think there is at least!). This question arises from a definition I formulated recently, and would like to ...

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### Are the pullback functors of adjoint functors also adjoint?

Given adjoint functors $F: A \to B$, $G: B \to A$, if you then take their pullback functors $F^* : Set^B \to Set^A$ and $G^* : Set^A \to Set^B$ given by pre-composition, are these two also adjoint ...