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Results tagged with topos-theory
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user 4613
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,...
19
votes
1
answer
876
views
Has this "backwards" perspective on toposes been studied?
Topos theory can be seen as a categorification of topology via the following analogies.
\begin{array}{|c|c|}
\hline
\text{locales}&\text{Grothendieck toposes}\\\hline
\text{open sets}&\text{sheaves}\ …
- 3,137
16
votes
2
answers
1k
views
Is there a universal way to force the Axiom of Choice to be true?
Given a model of set theory $V$ there are various ways to construct a model in which the Axiom of Choice holds, such as Gödel's constructible universe $L^V$ or by using forcing*. I'm wondering if any …
- 3,137
2
votes
What information is lost in $X \to \mathrm{Sh}(X)$?
Benjamin Steinberg's answer covers the case of topological spaces, so I'll answer this question for sites.
The functor
$$\mathrm{Sh}:\mathbf{Site}\rightarrow\mathbf{Topos}^{\mathrm{op}}$$
(here $\mat …
- 3,137