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Results tagged with topos-theory
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user 51164
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,...
9
votes
Accepted
Is Set a finitely presentable object in Topoi?
If $\mathcal{C}$ is a small category with finite limits then geometric morphisms from ${\rm Set}$ to the presheaf topos ${\rm PSh}(\mathcal{C})$ are in bijection with left exact functors $\mathcal{C} …
- 9,491
10
votes
Compact space in site -> compact object in topos
The question that you ask might be better phrased intrinsically without referring to sites. Fix an $0 \leq n \leq \infty$ and let $\mathbf{X}$ be an $n$-topos. Recall that an object $X \in \mathbf{X}$ …
- 9,491
7
votes
Accepted
What is a spectrum object in $\infty$-topoi?
Following up on the answer of Simon Henry, let us prove the following statement. For a pro-space $\hat{X} = \{X_i\}_{i \in I}$, we let $Spaces_{/\hat{X}}$ denote the $\infty$-topos defined as the (co …
- 9,491