added pointer to:

- Marta Bunge,
*Internal Presheaf Toposes*, Cahiers de topologie et géométrie différentielle catégoriques**18**3 (1977) 291-330 [numdam:CTGDC_1977__18_3_291_0]

The formulation In terms of external 2-sheaves works by passing to the 2-category of internal categories. In there you can do all of category theory and topos theory as you did externally.

]]>You can certainly have presheaves valued in locally internal categories over the base topos, see the last section of *internal diagram* (where this is detailed in the language of indexed categories). Using the internal language, these look exactly like ordinary non-Set-valued presheaves; so I’d guess that to obtain a sensible notion of a sheaf, one could simply formulate the usual sheaf condition in the internal language.

Do you see a direct way to expand the concept to an internal generalization of non-set valued sheaves ? In my understanding this entry generalizes the set-valued sheaves only.

]]>Thanks, much better! I agree it’s not a problem that the actual explicitness is one further click away.

]]>In this spirit I have also edited the very very last sentence of the entry (at then end of the References) making it now point to the two Definition-sections where previously it just vaguely referred to the explicit defintition. Good.

]]>Thanks!

I moved your new paragraph to become a subsection of the Definition-section, made my previous material there also a subsection, and added at the beginning of the Definition-section a little lead-in on how we will present two versions of the definition, one abstract, one more explicit.

Of course much of the explicitness of the second definition (the one you added) is out-sourced to the entry *internal diagram*- But I guess that’s okay.

I added the pedestrian definitions of *presheaf* and *sheaf* (as internal diagrams).

I have further expanded it (added two basic Propositions, more details in the definitions) and tried to prettify a bit more.

]]>created *internal sheaf*

Mainly it was bugging me that I didn’t find a piece of literature that said it quite explicitly the way I do there, so I wanted to have that written down. To be expanded, eventually.

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