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Todd has added to Grothendieck topos the statement and proof that any such is total and cototal (and I have added to adjoint functor theorem the statement that this implies that all (co)limit preserving functors between sheaf toposes have (right)left adjoints).
I notice that we should really merge Grothendieck topos with category of sheaves. But I don’t have the energy to do this now.
I would watch out about that merge, because “sheaf” need not mean a set-valued sheaf.
That’s true. But maye that’s one more reason to merge the content from category of sheaves into Grothendieck topos: because currently that’s all about set-valued sheaves.
Well, I just added a few words (in the Idea section) to presheaf to the effect that historically, the focus on set-valued sheaves came later, after all the developments in the 40’s and 50’s on things like sheaves of abelian groups. I think you have a point, but I’d like to think about it some more.
Okay, sure, we should do it correctly. We should keep both entries seperate. But it would be good not to spread out the material about sheaf toposes in two places in two parallel ways.
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