Re: Roos theorem

Re: Roos theorem

[Venkata Rayudu Posina]

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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