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2 votes
2 answers
172 views

Can the Category of that kind of small sets in $\sf NFU$ be Cartesian closed?

Working in Quine's $\sf NFU$, with urelements being at least as many as sets. Formally the latter is: $|Ur| \geq |Set|$. Where $Ur$ is the set of all urelements and $Set$ is the set of all sets. We ...
Zuhair Al-Johar's user avatar
3 votes
1 answer
599 views

Alternative definition of power object in a category

The standard definition of a power object seems to be: objects $\mathcal{P}X, K \in \mathbf{C}$ and a monic $\in: K \hookrightarrow X \times \mathcal{P}X$ such that for every monic $r: A \...
Jordan Barrett's user avatar
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 ...
Mike Shulman's user avatar
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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 ...
Tim Campion's user avatar
3 votes
1 answer
150 views

Internal characterizations of lifting properties?

This is basically a restatement of this question. Two arrows $f,g$ are orthogonal, i.e satisfy $f\perp g$, iff the square below is a pullback $$\require{AMScd} \begin{CD} \mathsf C(B,X) @>{f^\...
Arrow's user avatar
  • 10.5k
1 vote
1 answer
273 views

Do Categorical Quotients Preserve Covering Maps?

Before asking a question, please let me write down settings. SETTINGS: Let $C$ be a category with fiber products and $B$ be a closed subcategory of $C$ (i.e. $B$ contains any isomorphism of $C$, and ...
Hiro's user avatar
  • 945