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Results tagged with topos-theory
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user 10605
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,...
2
votes
Accepted
Local smallness and (higher) topoi
Consider a theory which has no models in $\mathrm{Set}$, but has a model in $\mathrm{Sh}(L)$ for some locale $L$. For example, the theory $\mathcal{CLF}$ of complete linearly ordered fields with more …
- 4,780
5
votes
Accepted
Isomorphism class of locally trivial object classified by some $H^1$ ?
It is a general fact that if you consider an abelian group $A$ in topos $T$, then equivalence classes of $A$-torsors in $T$ are classified by cohomology group $H^1(T;A)=Ext^1_T(\mathbb{Z},A)$. Here $\ …
- 4,780
5
votes
Examples of toposes for analysts
Besides the important examples of topoi already mentioned (like SDG), I would argue that the most important topos for any analyst is just the topos of sheaves on some topological space. I assume that …