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# Essential subtopoi of presheaf topoi

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(@matteocapucci)
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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

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(@matteocapucci)
Active Member
Joined: 2 years ago
Posts: 15
Topic starter

@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!

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