nLab defines a strict 2-groups in many different but equivalent ways, among them: an internal group object in Cat, an internal group object in Grpd Also, it is known that strict 2-groups may be ...
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 ...
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 ...
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 ...