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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
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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 (as …