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# Questions tagged [topos-theory]

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362 questions
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### What category of toposes is monadic over the 2-category of groupoids?

Excuse my lack of understanding of monadicity, but I have been looking at toposes and monads. I see Lambek showed that the category of Toposes are monadic over the category of categories. I see the ...
657 views

### Commutative rings : Topoi = Fields :?

The following is probably a bad question, but hopefully, it might have a very good answer. In category theory there is a quite famous analogy between topoi and commutative rings, I was never ...
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### Is Set a finitely presentable object in Topoi?

The setting for this question is the (2,1) category Topoi. 0-cells in Topoi are Grothendieck topoi. 1-cells are geometric morphisms and have the direction of the right adjoint. 2-cells are invertible ...
191 views

### Automorphism group of a torsor

Given a site $C$ and an object $U$, let $G$ be a sheaf of groups on this site and let $F$ be $G$-torsor, see the Stacks Project for the general definition. By restriction on the over category $C/U$ (...
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### Adjoints to forcing

Forcing over a partial order $P$ can be viewed in a category theoretic sense as constructing the presheaf topos ${\bf Set}^{P^{op}}$ over the partial order (viewed as a category) then passing through ...
624 views

### Toposophy vs Set theoretical multiverse philosophy

Johnstones classic topos theory book talks at some length in its introduction about how category theory/topos theory suggest that we view the 'universe' in which mathematics takes place as consisting ...
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### Universal property of sheaf category

Given a site $C$ with a Grothendieck topology and the category of presheaves $P(C)$ (either in the sense of presheaves of sets or in the $\infty$-sense), and the category $S(C)$ of sheaves with ...
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### Definition of $\in_c$ for power objects

On the nLab page for power objects, the object $\in_c$ is defined as the domain of a monomorphism $\in_c\hookrightarrow c\times\Omega^c$, and it is mentioned at the end of the article that in any ...
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### Reference Request: Cohomology and limits of coherent topoi. (Non-abelian case)

SGA 4 VI Discusses finiteness conditions one can impose on topoi to make limits behave correctly. I am not that familiar with SGA but it is my impression that this expose only discusses abelian ...
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### Topos with enough projectives

It is often observed that every presheaf topos has enough projectives, as a corollary of the result that representables are projective and every presheaf is a colimit of representables. We also have ...
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### Is there a version of the “infinitary” disjunctive normal form theorem for topoi and slice categories?

According to nLab Proposition 2.3. A complete Boolean algebra is completely distributive iff it is atomic (a CABA), i.e., is a power set as a Boolean algebra. This is basically an infinitary ...
335 views

### What is a spectrum object in $\infty$-topoi?

For any spectrum $E$, there is a "discrete" topos spectrum $(Spaces / E_n)_n$. And I believe any topos spectrum is a localization of a "discrete" one. Are there any "non-discrete" topos spectra? To ...

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