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Results tagged with ct.category-theory
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user 16857
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
4
votes
1
answer
979
views
Colimits in colimits of categories
I was considering the following situation. I have a directed/filtering system of categories $C_i$. I understand how take its direct limit (aka colimit) $C$ in the category of categories. My question i …
- 1,889
12
votes
Is it always possible to write a scheme as a colimit of affine schemes?
Yes. Let's assume your scheme $X$ has affine diagonal. This implies that, if $U_i$ is an affine open cover, then $U_{ij}$ is also an affine open cover.
Then $X$ is the co-equalizer you wrote.
However …
- 1,889
3
votes
Accepted
surjective morphism of schemes or epimorphism of sheaves?
I think (what currently is) Lemma 5.9 (tag 05VM) of the Algebraic Spaces chapter of the stacks project is exactly what we want.
Let F,G fppf sheaves and let $F \to G$ be a schematic, flat, locally of …
9
votes
1
answer
4k
views
surjective morphism of schemes or epimorphism of sheaves?
I have a technical question coming from reading Toen's master course on stacks.
If we view schemes as locally ringed spaces then there we could define a morphism to be surjective if it the underlying …
- 1,889