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Results tagged with topos-theory
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user 22810
A topos is a category that behaves very much like the category of sets and possesses a good notion of localization. Related to topos are: sheaves, presheaves, descent, stacks, localization,...
11
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0
answers
551
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The intrinsic meaning of abelian sheaf cohomology of a category
Basically my question is:
Suppose I meet an alien mathematician which understands everything through category theory and category theory alone. How would I convince said mathematician that certain …
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9
votes
1
answer
793
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Is the analytification functor part of a geometric morphism of topoi?
Let $Sh(\mathsf{\mathbb{C}-fAlg}^{op})$ be the topos of zariski sheaves on finitely genertaed $\mathbb{C}$-algebras.
A complex analytic space for our purpose is a locally ringed space locally isomor …
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9
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0
answers
376
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Is there any notion of "smoothification" from $\mathbb{R}$-schemes to generalized smooth spa...
I will write $\operatorname{Diff}$ to denote a category of generalized smooth spaces e.g. $Sh(\mathsf{CartSp})$. Is there a version of $\operatorname{Diff}$ for which there exists a functor $\mathcal{ …
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0
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1
answer
158
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If $J$-coverings can be glued $I$-locally is $J$-locality an $I$-local property? (Reducing d...
Let $(C,J)$ be a category with a grothendieck topology. For every object $X \in C$ there's (I hope) a little site which is the full subcategory of the slice category $C_{/X}$ whose objects are the mor …
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