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Small sheaves on large sites

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If you have a question about this talk, please contact Zhen Lin Low.

It is well known that the category of presheaves (of sets) on a small category is the free cocomplete category generated by the original small category; and restricting to a subcategory of sheaves is like imposing relations on the colimits so generated. Something similar is true for large categories, but one has to be much more careful. I will try to explain Shulman’s conditions for ensuring that the category of small sheaves on a large site satisfy Giraud’s axioms for a pretopos.

This talk is part of the Extraordinary Category Theory Seminar series.

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