All Questions
Tagged with cartesian-closed-categories topos-theory
6 questions
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 ...
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 \...
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 ...
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 ...
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^\...
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 ...