All Questions
Tagged with locally-presentable-categories topos-theory
5 questions
8
votes
1
answer
466
views
Tensor product of sites
Let $C, D$ two Grothendieck sites. Since the corresponding toposes $E, F$ are locally presentable categories, then (by Gabriel-Ulmer duality) they correspond to limit theories $X, Y$ (that is, small ...
- 6,962
9
votes
1
answer
478
views
From Topoi to Grothendieck categories
This question is mostly about a reference request. Let $\mathcal{E}$ be a Grothendieck topos. I am looking for a reference of the following two facts. I am aware that $(2) \Rightarrow (1)$ by Gabriel-...
- 9,111
16
votes
1
answer
584
views
When is the category of models of a limit theory a topos?
If $\mathcal{E}$ is a Grothendieck topos on a small base, then it is locally presentable, and hence is equivalent to the category of models of some limit theory.
Is there a characterization of ...
15
votes
2
answers
470
views
A locally presentable locally cartesian closed category that is not a quasitopos
This question asks for a locally presentable locally cartesian closed category that is not a topos. All the answers given (at least in the 1-categorical case) are quasitoposes. What is an example of ...
- 66.8k
7
votes
1
answer
452
views
Example of a locally presentable locally cartesian closed category which is not a topos?
The only way I know to get a locally cartesian closed category which is not a topos is to start with a topos and then throw out some objects so that the category is not sufficiently cocomplete to be a ...
- 64k