From: Ross Street <street@ics.mq.edu.au>
To: Andrew Stacey <andrew.stacey@math.ntnu.no>,
categories <categories@mta.ca>
Subject: Re: Bi-presheaves
Date: Sat, 7 Mar 2009 17:15:29 +1100 [thread overview]
Message-ID: <E1Lg66J-0002UT-8e@mailserv.mta.ca> (raw)
Given a category A, the Isbell envelope E(A) is the category whose
objects
are triplets (F_*, F^*, t) where F_* : A --> Set and F^* : A^{op} -->
Set are functors
and t_{a,b} : F^*(a) x F_*(b) --> A(a,b) is a family natural in a
and b in A. The
morphisms are as you described. There is a "double Yoneda" A --> E(A)
taking
c to (A(c,-), A(-,c), composition).
==Ross
On 06/03/2009, at 7:19 PM, Andrew Stacey wrote:
> When you say that you call it 'the Isbell envelope', what do you
> mean? Is the
> category the 'Isbell envelope of/on the original category' or are
> the objects
> 'Isbell envelopes' and we have the category of Isbell envelopes (in/
> on/of the
> original category)?
next reply other threads:[~2009-03-07 6:15 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-03-07 6:15 Ross Street [this message]
-- strict thread matches above, loose matches on Subject: below --
2009-03-10 8:50 Bi-presheaves Andrew Stacey
2009-03-08 19:25 Bi-presheaves Vaughan Pratt
2009-03-06 15:01 Bi-presheaves Bill Lawvere
2009-03-06 14:55 Bi-presheaves Bill Lawvere
2009-03-06 8:19 Bi-presheaves Andrew Stacey
2009-03-06 5:13 Bi-presheaves Ross Street
2009-03-05 15:34 Bi-presheaves Andrew Stacey
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