* Re: Bicomma objects
@ 2007-07-24 23:54 Stephen Lack
0 siblings, 0 replies; 2+ messages in thread
From: Stephen Lack @ 2007-07-24 23:54 UTC (permalink / raw)
To: categories
Dear Steve,
A bicomma object is a bicategorical limit, so determined only
up to equivalence. A comma object is a strict limit, so determined
up to isomorphism.
In the case of Cat, comma objects are just the usual comma categories
(strictly speaking, anything isomorphic to the comma category), while
anything equivalent to the comma category will be a bicomma object.
So any comma object is also a bicomma object, but the converse is false.
Moreover, there are 2-categories in which bicomma objects exist but
comma objects do not.
The situation with pullbacks, by the way, is slightly different. It is
not the case that every pullback is a bipullback (but there is a paper
of Joyal and Street giving a sufficient condition for a pullback to be
a bipullback).
Steve.
-----Original Message-----
From: cat-dist@mta.ca on behalf of Steve Vickers
Sent: Wed 25/07/2007 2:02 AM
To: categories@mta.ca
Subject: categories: Bicomma objects
What is the difference between a bicomma object and a comma object
(a.k.a. lax pullback)?
Steve.
^ permalink raw reply [flat|nested] 2+ messages in thread
* Bicomma objects
@ 2007-07-24 16:02 Steve Vickers
0 siblings, 0 replies; 2+ messages in thread
From: Steve Vickers @ 2007-07-24 16:02 UTC (permalink / raw)
To: categories
What is the difference between a bicomma object and a comma object
(a.k.a. lax pullback)?
Steve.
^ permalink raw reply [flat|nested] 2+ messages in thread
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