All Questions
Tagged with topos-theory adjoint-functors
8 questions
6
votes
1
answer
248
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Adjoints to inclusion pseudofunctors from topoi to Cat
Let's consider the bicategories, LogTopos of elementary topoi, logical functors and natural transformations and GrTopos of Grothendieck topoi, geometric morphisms and natural transformations.
The ...
- 1,347
8
votes
0
answers
221
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When is the Eilenberg-Moore category of a relative monad between two topoi a topos?
In the non-relative case, we have a theorem, that an Eilenberg-Moore category of algebras of a Monad $T$ on a topos is itself a topos if the monad in question has a right adjoint.
Now how does this ...
- 1,347
5
votes
0
answers
189
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When are topoi of coalgebras atomic?
A geometric morphism is atomic if its inverse image is logical. Now consider a Grothendieck topos $\varepsilon$ and its terminal geometric morphism $\Gamma : \varepsilon \rightarrow Set$, topos is ...
- 1,347
2
votes
0
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94
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What can be said about the free-forgetful adjunction of monad algebras with respect to topoi?
For a monad T on a topos E, if T has a right adjoint, then the Eilenberg-Moore category of algebras of T is equivalent to the co-Eilenberg-Moore category of co-algebras for the right adjoint comonad ...
- 1,347
3
votes
0
answers
83
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Cohesive structure of Cahiers and Dubuc topoi
The inclusion of commutative rings into supercommutative rings has two adjoints, one projecting out the even part and the other quotienting out the ideal generated by odd elements. After passing to ...
- 193
3
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0
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97
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When do geometric morphisms lead to periodic adjoints?
This may be a naïve question but I've been unable to locate a reference that addresses it. Any thoughts are appreciated!
Let $f:\mathcal{E}\to\mathcal{S}$ be a cohesive morphism of toposes. That is, ...
- 740
21
votes
1
answer
2k
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Surmounting set-theoretical difficulties in algebraic geometry
The category $\text{AffSch}_S$ of affine schemes over some base affine scheme $S$ is not essentially small. This lends itself to certain set-theoretical difficulties when working with a category $Sh(\...
- 3,019
10
votes
0
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317
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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 ...
- 10.1k