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

2 votes
0 answers
185 views

Relation between push forward by diagonal morphism and higher direct image functors

Let $f : X \to Y$ be a morphism between two Noetherian schemes. Then $f_*$(respect to $R^1f_*$) sends coherent sheaves to coherent sheaves if and only if $f$ is universally closed (respect to separat …
Doyoung Choi's user avatar
2 votes
0 answers
115 views

About condition for structure sheaf of a scheme being compact object in a category of sheaf ... [duplicate]

I found the condition for one direction : Categorical interpretation of quasi-compact quasi-separated schemes This article said that if $X$ is quasi compact and quasi separated, $\mathscr{O}_X$ is a c …
Doyoung Choi's user avatar