From: Jocelyn Paine <popx@j-paine.org>
To: David Leduc <david.leduc6@googlemail.com>
Cc: categories <categories@mta.ca>
Subject: Re: Evil in bicategories
Date: Sun, 12 Sep 2010 07:03:41 +0100 (BST) [thread overview]
Message-ID: <E1OusQm-0001pV-MP@mlist.mta.ca> (raw)
In-Reply-To: <E1OuQsT-0003hL-P6@mlist.mta.ca>
On Sat, 11 Sep 2010, David Leduc wrote:
> In a bicategory, composition of 1-cells is associative up to
> isomorphism. Because it would be evil to insist that h o (g o f) is
> equal to (h o g) o f. However the source and target objects of those
> compositions must be equal. Isn't it evil? Why not weaken this
> requirement by saying that the sources (respectively, targets) of h o
> (g o f) and (h o g) o f must only be isomorphic?
>
Your question made me wonder why the axioms for ordinary categories, i.e.
1-categories, insist that in composing f:A->B and g:C->D, B and C must be
equal. Isn't it just as evil not to allow them to be merely isomorphic?
Jocelyn Paine
http://www.j-paine.org
Jocelyn's Cartoons:
http://www.j-paine.org/blog/jocelyns_cartoons/
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-09-12 6:03 UTC|newest]
Thread overview: 16+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-09-11 2:05 David Leduc
2010-09-11 23:23 ` Toby Bartels
2010-09-12 1:28 ` David Roberts
2010-09-12 6:03 ` Jocelyn Paine [this message]
[not found] ` <20100911232358.GA32145@ugcs.caltech.edu>
2010-09-12 6:27 ` David Leduc
[not found] ` <AANLkTimbfG0tkjSNZgjL2yADBHnKAXQiHYsAkioEnxJY@mail.gmail.com>
2010-09-12 7:31 ` Toby Bartels
[not found] ` <20100912073136.GA9115@ugcs.caltech.edu>
2010-09-12 10:22 ` David Leduc
[not found] ` <AANLkTi=ZLdVcbvaHPaCfaZhzyDYCdwLNUQTj-5fNZ4p4@mail.gmail.com>
2010-09-12 17:13 ` Toby Bartels
2010-09-12 12:38 ` JeanBenabou
2010-09-13 0:16 ` David Roberts
2010-09-13 22:28 ` Toby Bartels
2010-09-14 22:32 ` Richard Garner
2010-09-14 15:09 ` Miles Gould
2010-09-12 16:52 ` Peter LeFanu Lumsdaine
2010-09-14 6:28 Michael Shulman
2010-09-15 1:12 Vaughan Pratt
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