From: Marco Grandis <grandis@dima.unige.it>
To: categories@mta.ca
Subject: Re: weak double categories?
Date: Fri, 28 Oct 2005 13:32:04 +0200 [thread overview]
Message-ID: <633CF610-8823-4F2D-BF2F-63911C9E13A9@dima.unige.it> (raw)
In-Reply-To: <E1EVEI7-0001JV-6G@mailserv.mta.ca>
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The definition of weak (or pseudo) double category is what you would =20
expect, once you know the strict case and the definition of =20
bicategory; think of a "pseudocategory object in Cat". It has =20
probably been in the categorical folklore since quite a while.
You can find it (including the machinery of lax double functors, =20
horizontal and vertical transformations, etc.) in two papers in =20
Cahiers, where part of the general theory of weak double categories =20
has been developed
M. Grandis - R. Pare, Limits in double categories, Cah. Topol. =20
Geom. Diff. Categ. 40 (1999), 162-220,
- -, Adjoints for double categories, Cah. Topol. Geom. Diff. =20
Categ. 45 (2004), 193-240.
Other papers on (weak) double categories, many of them by Bob Pare et =20=
al., are referred to in the articles above.
In book form
Tom Leinster, Higher operads, higher categories, Cambridge Un. =20
Press 2004,
has Section 5.2, devoted to weak double categories.
Best regards
Marco
Marco Grandis
Dipartimento di Matematica
Universit=E0 di Genova
Via Dodecaneso, 35
16146 Genova
Italy
e-mail: grandis@dima.unige.it
tel: +39 010 353 6805
http://www.dima.unige.it/~grandis/
On 26 Oct 2005, at 22:08, John Baez wrote:
> Dear Categorists -
>
> If you weaken the notion of 2-category you get the notion of
> bicategory. Has anyone tried to correspondingly weaken the
> notion of double category, so that a bicategory is a special
> sort of "weak double category" in analogy to the ways in which
> a 2-category is a special sort of double category? Did anyone
> succeed?
>
> Best,
> jb
>
>
>
>
>
>
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next prev parent reply other threads:[~2005-10-28 11:32 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2005-10-26 20:08 John Baez
2005-10-27 21:55 ` Tom Leinster
2005-10-28 9:10 ` Richard Garner
2005-10-28 11:32 ` Marco Grandis [this message]
2005-10-28 0:13 Ross Street
2005-10-28 21:07 John Baez
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