Tagged Questions

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right adjoint functor for closed immersion of topoi

Let $i\colon (X,A)\rightarrow (Y,B)$ be a closed immersion of ringed topoi. Does functor $i_*\colon Mod(A)\rightarrow Mod(B)$ have a right adjoint?
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questions of localization of topos

Let $T$ be a topos, and $F \in T$, $T/F$ a localization of $T$. So we have a natural morphism $i: T/F \longrightarrow T$. My questions are: 1.What are the definitions of $i_{\ast}$ and $i^{\ast}$ ...
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Extracting internal sites of definition

Given sites $(C,J)$ and $(D,K)$, and a functor $f\colon C\to D$ satisfying the covering lifting property: For every object $c$ of $C$ and $K$-covering sieve $S$ of $f(c)$, there is a $J$-covering ...
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What can be expressed in and proved with the internal logic of a topos?

The title of this post expresses what I really want, which is to learn how to wield the internal logic of a topos more effectively. However, to bring it down to earth, I'll ask a few basic questions ...
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When does the direct image functor nicely push past the power/exists functor?

Let $D$ and $E$ be toposes and let $f_{\ast}\colon D\to E$ be the direct image part of a geometric morphism $(f^{\ast},f_{\ast})$ between them. Considered as categories, we have (covariant) ...
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Connections between topos theory and topology

What are some "applications to" / "connections with" topology that one could hope to reasonably cover in a first course on topos theory (for master students)? I have an idea of what parts of the ...
Suppose that $\mathcal{E}$ is a (Grothendieck) topos. It carries a (large) Grothendieck topology (in fact the canonical topology), a basis of which is determined by declaring a collection of morphisms ...
What is an $(\infty,1)$-topos, and why is this a good setting for doing differential geometry?
In this post on the n-Category Café, Urs Schreiber says that, "The theory of G-principal bundles makes sense in any $(\infty,1)$-topos." I followed the link to the nLab and tried to chase definitions, ...