CAUTION: The Sender of this email is not from within Dalhousie. If I may, I'd like to add to my earlier question regarding the conditions under which C = B^A the following: If A and B are adequate and discrete, respectively, subcategories of C, then objects of C can be represented as contravariant functors A --> B. Please correct me if I'm mistaken. Also, is this related to the theorem of Roos in SGA4? thank you, posina On Wed, Dec 2, 2020 at 3:48 PM Venkata Rayudu Posina < posinavrayudu@gmail.com> wrote:

Dear All,

I hope and pray you and your family are all safe and well.

I was wondering under what conditions a category C can be written as an exponential B^A (a category of contravariant functors interpreting a theory A into a background B). Reyes, Reyes, and Zolfaghari note (on p. 81 of their book: Generic Figures and their Glueings) that the answer to the above question is a theorem of Roos in SGA4, p. 415.

Would you be kind enough to direct me to an English version of Roos

theorem.

thank you, posina

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