From: grandis@dima.unige.it (Marco Grandis)
To: categories@mta.ca, James Stasheff <jds@math.unc.edu>
Subject: Re: terminology
Date: Fri, 28 Jan 2000 10:57:40 +0100 [thread overview]
Message-ID: <v02140b01b4b70433e385@[130.251.60.168]> (raw)
J. Stasheff wrote:
>Has terminology settled down?
>I can recall seeing various terms for
>``simplicial object without degeneracies''
I am afraid it has not.
In my opinion, it should be called 'semi-simplicial object', consistently
with the original terminology in Eilenberg-Zilber (see references below).
Such a term has been adopted in Weibel's text on homological algebra
(1994). But there seems to be some opposition.
___
I hope the following reconstruction of terminology is correct.
1. What is now called a simplicial object was introduced by Eilenberg and
Zilber (1950); they use:
(a) [already existing] 'simplicial complex' = set with distinguished parts;
(b) [new term] 'semi-simplicial complex' = graded set with faces;
(c) [new term] 'complete s.s. complex' = graded set with faces and degeneracies;
2. Later, notion (c) was recognised as more important than (b) and called
'semi-simplicial complex', leaving (b) without any standard name.
3. Since May's book (1967) at least, notion (c) gradually settled down as
'simplicial set', generalised to 'simplicial object' in a category; this is
now standard.
4. It should now be natural to use a similar term, 'semi-simplicial object
(possibly: set)' for (b), i.e. a 'simplicial object without degeneracies'
(as in Weibel 1994). This is consistent with the original use in
Eilenberg-Zilber and gives a non-ambiguous set of terms for the three
notions recalled:
(a) 'simplicial complex' (also: combinatorial complex)
(b) 'semi-simplicial object (set)'
(c) 'simplicial object (set)'
However, I used myself this terminology in a paper published in '97 and had
strong reactions from people attached to the terminology in use between
50's and '60s (point 2 above).
___
References:
S. Eilenberg - J.A. Zilber, Semi-simplicial complexes and singular
homology, Ann. of Math. 51 (1950), 499-513.
J.P. May, Simplicial objects in algebraic topology, Van Nostrand 1967.
C.A. Weibel, An introduction to homological algebra, Cambridge Univ. Press,
Cambridge, 1994.
___
With best regards
Marco Grandis
Dipartimento di Matematica
Universita' di Genova
via Dodecaneso 35
16146 GENOVA, Italy
e-mail: grandis@dima.unige.it
tel: +39.010.353 6805 fax: +39.010.353 6752
http://www.dima.unige.it/STAFF/GRANDIS/
ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/
next reply other threads:[~2000-01-28 9:57 UTC|newest]
Thread overview: 64+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-01-28 9:57 Marco Grandis [this message]
-- strict thread matches above, loose matches on Subject: below --
2017-02-11 20:42 Terminology Fred E.J. Linton
2017-02-14 8:48 ` Terminology Steve Vickers
[not found] ` <02568D97-0A72-4CA8-8900-BDE11E890890@cs.bham.ac.uk>
2017-02-14 9:39 ` Terminology Jean Benabou
2017-02-09 22:03 Terminology Andrée Ehresmann
2017-02-08 8:03 Terminology Jean Benabou
2017-02-08 16:34 ` Terminology Jirí Adámek
2017-02-10 1:42 ` Terminology George Janelidze
2017-02-08 21:40 ` Terminology Carsten Führmann
2017-02-09 11:31 ` Terminology Thomas Streicher
[not found] ` <20170208180636.18346065.28939.42961@rbccm.com>
2017-02-09 16:38 ` Terminology Jean Benabou
2017-02-11 15:07 ` Terminology Steve Vickers
2013-05-02 3:57 Terminology Fred E.J. Linton
2013-05-03 11:53 ` Terminology Robert Dawson
2013-05-02 3:57 Terminology Fred E.J. Linton
2013-04-30 1:20 Terminology Fred E.J. Linton
2013-04-24 17:13 Terminology Jean Bénabou
2013-04-24 23:04 ` Terminology David Roberts
2013-04-27 13:08 ` Terminology Thomas Streicher
[not found] ` <20130427130857.GC16801@mathematik.tu-darmstadt.de>
2013-04-28 3:49 ` Terminology Jean Bénabou
2013-04-28 22:47 ` Terminology Olivier Gerard
[not found] ` <557435A6-4568-4012-8C63-E031931F41FB@wanadoo.fr>
2013-04-28 14:17 ` Terminology Thomas Streicher
2013-04-29 20:05 ` Terminology Toby Bartels
2013-04-30 0:58 ` Terminology Peter May
2010-09-29 2:03 terminology Todd Trimble
2010-09-28 4:38 terminology Eduardo J. Dubuc
2010-05-27 18:31 terminology Colin McLarty
2010-05-19 10:38 Re terminology: Ronnie Brown
2010-05-20 7:58 ` soloviev
2010-05-20 19:53 ` terminology Eduardo J. Dubuc
[not found] ` <AANLkTikre9x4Qikw0mqOl1qZs9DDSkcBu3CXWA05OTQT@mail.gmail.com>
2010-05-21 17:00 ` Re terminology: Ronnie Brown
[not found] ` <B3C24EA955FF0C4EA14658997CD3E25E370F5827@CAHIER.gst.uqam.ca>
2010-05-22 21:43 ` terminology Ronnie Brown
[not found] ` <4BF84FF3.7060806@btinternet.com>
2010-05-22 22:44 ` terminology Joyal, André
2010-05-23 15:39 ` terminology Colin McLarty
2010-05-24 18:04 ` terminology Vaughan Pratt
2010-05-26 3:08 ` terminology Toby Bartels
2010-05-25 14:08 ` terminology John Baez
2010-05-26 8:03 ` terminology Reinhard Boerger
2010-05-25 19:39 ` terminology Colin McLarty
2010-05-29 21:47 ` terminology Toby Bartels
2010-05-30 19:15 ` terminology Thorsten Altenkirch
[not found] ` <A46C7965-B4E7-42E6-AE97-6C1D930AC878@cs.nott.ac.uk>
2010-05-30 20:51 ` terminology Toby Bartels
2010-06-01 7:39 ` terminology Thorsten Altenkirch
2010-06-01 13:33 ` terminology Peter LeFanu Lumsdaine
[not found] ` <7BF50141-7775-4D3C-A4AF-D543891666B9@cs.nott.ac.uk>
2010-06-01 18:22 ` terminology Toby Bartels
[not found] ` <AANLkTilG69hcX7ZV8zrLpQ_nf1pCmyktsnuE0RyJtQYF@mail.gmail.com>
2010-05-26 8:28 ` terminology John Baez
2010-05-16 12:44 terminology Peter Selinger
2010-05-13 17:17 bilax_monoidal_functors Michael Shulman
2010-05-14 14:43 ` terminology (was: bilax_monoidal_functors) Peter Selinger
2010-05-15 19:52 ` terminology Toby Bartels
2010-05-08 3:27 RE : bilax monoidal functors John Baez
2010-05-10 18:16 ` bilax_monoidal_functors?= John Baez
2010-05-11 8:28 ` bilax_monoidal_functors?= Michael Batanin
2010-05-12 3:02 ` bilax_monoidal_functors?= Toby Bartels
2010-05-13 23:09 ` bilax_monoidal_functors?= Michael Batanin
2010-05-15 16:05 ` terminology Joyal, André
2007-01-27 17:06 terminology wlawvere
2007-01-26 23:30 terminology Eduardo Dubuc
2005-12-30 1:16 terminology vs27
2005-12-29 19:09 terminology Nikita Danilov
2005-12-10 3:51 Terminology jean benabou
2005-12-21 20:04 ` Terminology Eduardo Dubuc
2005-12-26 19:47 ` terminology Vaughan Pratt
2005-12-29 23:17 ` terminology Eduardo Dubuc
2006-01-04 14:59 ` terminology Eduardo Dubuc
2003-10-17 15:19 terminology Marco Grandis
2003-10-16 21:39 terminology James Stasheff
2001-04-09 11:06 Terminology Krzysztof Worytkiewicz
2000-12-14 6:17 Terminology Max Kelly
[not found] <3a35cdd73a39f901@amyris.wanadoo.fr>
2000-12-13 11:10 ` Terminology Dr. P.T. Johnstone
2000-12-13 1:17 Terminology Steve Lack
2000-12-12 8:19 Terminology Jean Benabou
2000-01-28 12:02 terminology James Stasheff
2000-01-27 19:28 terminology James Stasheff
2000-01-27 21:04 ` terminology Paul Glenn
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