The internalization tag has no usage guidance.

**11**

votes

**1**answer

252 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 ...

**6**

votes

**2**answers

502 views

### On internal functions and arrows in a Topos

I am not an expert on elementary topos (meaning by this to work with the internal language in a Grothendiek topos) and I rather be told than struggle with the following:
Consider an elementary topos ...

**12**

votes

**1**answer

536 views

### What are the smooth manifolds in the topos of sheaves on a smooth manifold?

The category of internal locales in the Grothendieck topos of sheaves on a locale X
is equivalent to the slice category over X.
In other words, internal locales over X are precisely morphisms of ...