# Tagged Questions

**10**

votes

**1**answer

217 views

### Pullback-stability of internally projective objects

An object $X$ of a category $C$ is said to be projective if the hom-functor $C(X,-)$ preserves epimorphisms (or, in general, some restricted class of epimorphisms such as the regular or effective ...

**1**

vote

**1**answer

358 views

### Counterexemple to Urysohn's lemma in a topos without denombrable choice ?

Hello !
The Urysohn's Lemma assert that in every topological spaces which is normal two closed subset may be separated by a real valued function. It's proof use axiom of countable choice (but not the ...

**5**

votes

**2**answers

483 views

### Example of a topos that violates countable choice

At this nLab page we have the line
In contrast, any topos that violates countable choice, of which there are plenty, must also violate internal COSHEP.
It doesn't give an example, and neither ...