Re: Bi-presheaves

[Bill Lawvere <wlawvere@buffalo.edu>]

Dear Andrew Stacey,

    When John Isbell introduced this construction in the early
1960's, he called it the 'double envelope', so I often call
it the Isbell envelope.
    You just re-discovered it!

Bill Lawvere



************************************************************
F. William Lawvere, Professor emeritus
Mathematics Department, State University of New York
244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
Tel. 716-645-6284
HOMEPAGE:  http://www.acsu.buffalo.edu/~wlawvere
************************************************************



On Thu, 5 Mar 2009, Andrew Stacey wrote:

> Dear Categorists,
>
> I'm interested in looking at the following type of thing:
>
> Start with an essentially small category, T, and look at the category whose
> objects are triples (P,F,c) where: P is a contravariant functor T -> Set, F is
> a covariant functor T -> Set and c is a natural transformation from P x F to
> the Hom bi-functor.  Morphisms are pairs of natural transformations P_1 -> P_2
> and F_2 -> F_1 that intertwine the natural transformations c_1 and c_2.
>
> One could also enrich the whole structure.
>
> Has this cropped up anywhere before?  If so, what is it called and where can
> I learn about it?  If not, what shall I call it?
>
> If this is something standard then please pardon my ignorance.  I'm fairly new
> to _real_ category theory and am still just learning the basics.
>
> Thanks,
>
> Andrew Stacey
>
>
>
>