From: Colin McLarty <colin.mclarty@case.edu>
To: categories@mta.ca
Subject: Re: terminology
Date: Thu, 27 May 2010 14:31:03 -0400 [thread overview]
Message-ID: <E1OIObw-0005c2-PS@mailserv.mta.ca> (raw)
Yes, Michael has said in several papers that his foundation would be
given in FOLDS. And perhaps some specific version of the axioms has
been given in some paper that I have missed. But I do not know of it;
and when Martin-Löf suggested last year that I might want to pursue a
type-theoretic foundation for category theory he did not mention
knowing of one existing yet. So far as I know it remains a project.
best, Colin
2010/5/26 John Baez <baez@math.ucr.edu>:
> Colin wrote:
>
>
> As to articulating a way to avoid ever using identity of objects and
>> identity of categories, John Baez writes
>>
>>> I think Michael Makkai has done it. He has formulated a foundational
>>> approach to mathematics based on infinity-categories, in which equality
>>> plays no fundamental role:
>>>
>>> http://www.math.mcgill.ca/makkai/mltomcat04/mltomcat04.pdf
>>>
>>> I think some approach along these general lines might ultimately become
>> quite popular.
>>
>> But so far as know, this remains an approach, and not any specific set of
>> axioms offered as foundation.
>>
>
>
> I should let Michael speak for himself, but I have the impression that he
> intends to found all his work on FOLDS - "first-order logic with dependent
> sorts". In this paper:
>
> http://www.math.mcgill.ca/makkai/folds/foldsinpdf/FOLDS.pdf
>
> he writes:
>
> "The restriction on the use of equality in FOLDS is a fundamental feature.
> FOLDS is to be used in formulating categorical situations in which, for
> example, equality of objects of a category is not an admissible primitive.
> The absence of term-forming operators, to be interpreted as
> functions, is a consequence of the absence of equality; it seems to me that
> the notion of "function" is incoherent without equality.
>
> It is convenient to regard FOLDS a logic without equality entirely, and deal
> with equality, as much as is needed of it, as extralogical primitives."
>
> Best,
> jb
>
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next reply other threads:[~2010-05-27 18:31 UTC|newest]
Thread overview: 64+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-05-27 18:31 Colin McLarty [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
2010-05-19 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
2000-01-28 9:57 terminology Marco Grandis
2000-01-27 19:28 terminology James Stasheff
2000-01-27 21:04 ` terminology Paul Glenn
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