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Results tagged with topos-theory
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user 76299
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,...
7
votes
1
answer
161
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When is the category of sheaves on a site compactly assembled/a continuous category?
If $(C,J)$ is a site, what is a natural condition on the Grothendieck topology $J$ to ensure that the category $Sh(C,J)$ is compactly assembled? I am both interested in the 1-categorical as well as th …
- 2,303
24
votes
1
answer
1k
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Examples of $(\infty,1)$-topoi that are not given as sheaves on a Grothendieck topology
An $(\infty,1)$-topos according to Lurie is defined as (accessible) left exact localization of a presheaf $(\infty,1)$-category $\text{P}(\mathcal C)$.
Those $(\infty,1)$-topoi $\text{Sh}(\mathcal C)$ …
- 2,303
29
votes
2
answers
4k
views
The philosophy behind local rings
This question has been bugging me for a while and I can't seem to make sense of it on a clear conceptual level.
The theory of local rings is given by taking the theory of rings and adding the axioms
…
- 2,303
5
votes
0
answers
157
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Resources on a smooth topos containing complex analytic/holomorphic geometry
In this question Urs Schreiber mentioned there are models in synthetic differential geometry of complex analytic geometry.
First of all: When Urs writes complex analytic geometry, does he mean comple …
- 2,303
25
votes
1
answer
2k
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A geometric theory of Blueprints? (Algebras over the field with one element)
In my attempt to tackle the various approaches of defining algebraic geometry over $\mathbb F_1$, I was just reading through Lorscheid's paper The geometry of blueprints. I certainly like the idea a l …
- 2,303