--- Sab 25/8/12, Fred E.J. Linton <fejlinton@usa.net> ha scritto:
Da: Fred E.J. Linton <fejlinton@usa.net> Oggetto: Re: categories: question on terminology A: "claudio pisani" <pisclau@yahoo.it>, categories@mta.ca Data: Sabato 25 agosto 2012, 05:35 Claudio Pisani asked,
Is there a standard name for those presheaves X on a category C such that Xf is a bijection for any f in C?
Well, those presheaves are exactly the "restrictions to C" of the presheaves on the grouppoid reflection (the grouppoidal 'quotient') of C (by which I mean the category got by declaring invertible every C-morphism).
Does that suggest "grouppoidal action of C" might work? I think I'd tend to lobby against the use of the prefix "bi-" unless there were *really* compelling reasons in favor of it.
Cheers, -- Fred
Dear Fred, thanks for the suggestion. It seems to me that its disadvantage is that "groupoidal action of C" may suggest that C itself is a groupoid, but probably the ambiguity disappears in the right context. By the way, I am actually interested in the (full and faithful, indexed) inclusion of presheaves on C' (where C' is the groupoid reflection of C) in presheaves on C and C^op (that is of groupoidal actions in left and in right actions). In fact it seems to provide a useful link between left and right actions. Claudio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]