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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
3
votes
Accepted
Descent of Morphisms of Sheaves
Yes, the property is satisfied (note that $\Gamma(Y,f^{-1}A)=A(f(Y))$, since $f$ is open). I didn't read the book, but I imagine that the point is not to give a strange definition of a sheaf on a topo …
2
votes
Category Theory and Ergodic Theory
There is this post, and its continuation