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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

2 votes
0 answers
131 views

A functor preserving adjunction between functor categories

I have the following problem. Let $\mathcal{C}_0$, $\mathcal{C}$ be small categories and $\mathcal{D}$, $\mathcal{E}$ be locally small categories. Let $Q\colon \mathcal{C}_0\to \mathcal{C}$ be a funct …
4 votes
1 answer
320 views

Isomorphism of coends

This is a follow-up to this question: Reduction to graph subgroups for Bredon homology when the $G_1\times G_2$ is $G_2$-free In his (very nice) answer Gregory Arone stated the following fact. Let $Q: …
8 votes
1 answer
228 views

Class of maps in localized category may not be a set

In one of the very first sentences in Hovey's "Model Categories", Ist chapter, we read that One can always invert these "weak equivalences" formally , but there is a foundational prob …