I have a complete Boolean algebra, and I'd like to show sheaves over it (wrt the usual coverage of jointly surjective families) are a level of the presheaves over it. I need that left adjoint to sheafification!
Is there some general useful fact about the existence of left adjoints to sheafification? This is equivalent to ask what are the levels of a presheaf topos
@ocaramello Uh, I see! Indeed, you/your slides never refer to objects. I mistakenly went for a subcategory, which includes identities, hence objects, but now I understand that's not strictly necessary!