From: "Lutz Schröder" <Lutz.Schroeder@dfki.de>
To: Emily Riehl <eriehl@math.harvard.edu>, categories <categories@mta.ca>
Subject: Re: partial categories
Date: Thu, 29 Sep 2011 14:24:27 +0200 [thread overview]
Message-ID: <E1R9FsZ-0004RA-3c@mlist.mta.ca> (raw)
In-Reply-To: <E1R92mj-0001a9-J1@mlist.mta.ca>
I studied these things in my PhD work. The thesis itself is in German,
I'm afraid, but there's a series of papers based on it which you can
find on my homepage. Maybe the most interesting one for you might be the
paper with Mateus on probabilistic automata (which form a certain type
of partial category) in MSCS 12 (2002), pp. 481–512.
Regards,
Lutz
Am 28.09.2011 22:34, schrieb Emily Riehl:
> 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
>
--
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Prof. Dr. Lutz Schröder
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Safe and Secure Cognitive Systems
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next prev parent reply other threads:[~2011-09-29 12:24 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-09-28 20:34 Emily Riehl
[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 [this message]
2011-09-30 7:38 ` Reference requested David Roberts
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