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Categories in which finite powers commute with filtered colimits

If $\mathcal{C}$ is a category with finite products and filtered colimits, then we say that finite powers commute with filtered colimits in $\mathcal{C}$ if for each natural number $n$, the $n$th ...
User7819's user avatar
  • 203
5 votes
2 answers
217 views

When is a locally presentable category (locally) cartesian-closed?

Let $\kappa$ be a regular cardinal. A category $\mathscr C$ is locally $\kappa$-presentable iff it is the free completion of a small $\kappa$-cocomplete category under $\kappa$-filtered colimits. Is ...
varkor's user avatar
  • 7,889
14 votes
2 answers
435 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 ...
Mike Shulman's user avatar
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6 votes
1 answer
380 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 ...
Tim Campion's user avatar
  • 59k
4 votes
1 answer
440 views

Example of a non-closed cocomplete symmetric monoidal category

Background By a cocomplete symmetric monoidal category $C$ I mean a symmetric monoidal category whose underlying category is cocomplete and such that $- \otimes X : C \to C$ is cocontinuous for all $X ...
Martin Brandenburg's user avatar