From: Emily Riehl <eriehl@math.harvard.edu>
To: categories@mta.ca
Subject: partial categories
Date: Wed, 28 Sep 2011 16:34:30 -0400 (EDT) [thread overview]
Message-ID: <E1R92mj-0001a9-J1@mlist.mta.ca> (raw)
A colleague of mine is wondering if anyone has studied "partial
categories," by which she means directed graphs with identities but with
only some compositions (including all identity compositions) defined.
A partial category can be thought of as a category enriched in pointed
sets (with smash product as tensor and S^0 as unit). The slogan is that
the basepoint in each hom-set stands in for "does not exist". But enriched
functors don't give the right notion of maps; these should preserve
identities and all specified compositions. Enriched functors behave
appropriately with regards to the identites but may "forget" extant
arrows and in particular need not preserve composites. So perhaps this
perspective is not useful.
I'll happily pass along any suggestions.
Thanks,
Emily Riehl
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2011-09-28 20:34 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-09-28 20:34 Emily Riehl [this message]
[not found] ` <CADxNEA2=AdiLetth8HkP0LK2Y8chP0kfrTjyQ5bP1OTA3h5Fig@mail.gmail.com>
2011-09-29 1:11 ` Claudio Hermida
2011-09-29 1:35 ` Reference requested Peter May
2011-09-29 13:41 ` Ronnie Brown
2011-09-30 7:34 ` jpradines
[not found] ` <11E807BD-8A2D-423D-8D1B-117BC99B7CF8@mq.edu.au>
2011-09-30 13:56 ` Peter May
2011-09-29 2:18 ` partial categories Peter Selinger
2011-09-29 12:24 ` Lutz Schröder
2011-09-30 7:38 ` Reference requested David Roberts
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