From: Joachim Kock <kock@mat.uab.es>
To: categories@mta.ca
Subject: Re: Semigroups with many objects
Date: Fri, 25 Nov 2005 22:24:37 +0100 [thread overview]
Message-ID: <a06100510bfad07f73a7a@[192.168.1.7]> (raw)
In-Reply-To: <281.4f1b3b.30b73c65@aol.com>
>Is there an accepted terminology for semigroups with many objects, i.e.
>gadgets that satisfy the all the axioms satisfied by categories excepting those which refer to identities ?
Perhaps 'semi-category' is the most widely used term.
The word 'taxonomy' has also been used (Paré, Wood, Ageron), but
Koslowski has used that word for something a bit more complicated
('interpolads in SPAN').
On the other hand, Schroeder has used the word 'semi-category'
for the 'multiplicative graphs' of Ehresmann (some structure where
composition of arrows is not always defined even if their source
and target match). (Curiously, in a preliminary version of the paper
by Moens, Berni-Canani, and Borceux, 'On regular presheaves and
regular semi-categories', the term 'multiplicative graph' was used
for 'semi-category' -- the final version uses 'semi-category'.)
I would also like to advogate 'semi-monoid' instead of 'semi-group',
and 'semi-monoidal category' for 'monoidal category without unit'.
It seems to be too late at this point to convince operadists to say
'semi-operad' for operads without unit.
In the same spirit I find it convenient to use 'semi-simplicial set'
for presheaves on Delta-mono, but I am told that this is confusing,
since apparently 'semi-simplicial set' meant something else fifty
years ago...
Cheers,
Joachim.
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Joachim Kock <kock@mat.uab.es>
Departament de Matemàtiques -- Universitat Autònoma de Barcelona
Edifici C -- 08193 Bellaterra (Barcelona) -- ESPANYA
Phone: +34 93 581 25 34 Fax: +34 93 581 27 90
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next prev parent reply other threads:[~2005-11-25 21:24 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2005-11-24 15:55 Topos8
2005-11-25 3:56 ` duraid
2005-11-25 21:24 ` Joachim Kock [this message]
2005-11-25 3:34 Topos8
2005-11-25 17:51 ` Miles Gould
2005-11-26 4:30 Philippe Gaucher
2005-11-30 15:51 ` Lutz Schroeder
2005-11-26 14:49 Topos8
2005-11-28 12:26 semigroups " Peter Freyd
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