From: Urs Schreiber <urs.schreiber@googlemail.com>
To: "Joyal, André" <joyal.andre@uqam.ca>
Subject: Re: Straw man terminology
Date: Thu, 27 May 2010 10:44:20 +0200 [thread overview]
Message-ID: <E1OIOWY-0005Re-PM@mailserv.mta.ca> (raw)
Dear Andre,
> I agree that Lurie is using the infinity-n-category terminology.
> I am not questioning that.
> I am observing that he is calling a quasi-category an infinity-category.
> In his terminology, an infinity-category is a special kind of
> infinity-one-category.
>
> I believe that the name infinity-category should apply to all "infinity"
> categories,
> inculding the infinity-one-category. No?
Yes, I entirely agree with that. In our discussion I did not promote
Jacob Lurie's use of "oo-category" for "quasi-category", What I did
and do promote is to use
* "oo-groupoid" and "(oo,0)-category" as the term for the abstract
concept which is equivalently realized by Kan complexes, simplicial
groupoids, topological spaces, etc. and has special strict models by
strict omega-groupoids, oo-fold groupoids etc.
* "(oo,1)-category" as the term for the abstract concept which is
equivalently realized by quasi-categories, Kan-complex enriched
categories, complete Segal spaces, Segal categories, categories with
weak equivalences, (oo,1)-theta spaces, etc.
* "(oo,n)-category" as the term for the abstract concept which is
equivalently realized by n-fold complete Segal spaces, (oo,n)-Theta
spaces etc.
Best,
Urs
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2010-05-27 8:44 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-05-27 8:44 Urs Schreiber [this message]
[not found] <AANLkTimkcg8A7yvuwGUgijWkkzXRFqkYU6o3kY5GXdP1@mail.gmail.com>
2010-05-27 3:31 ` Joyal, André
-- strict thread matches above, loose matches on Subject: below --
2010-05-26 17:59 Urs Schreiber
2010-05-27 22:28 ` jim stasheff
2010-05-27 22:30 ` jim stasheff
2010-05-22 16:42 Peter May
2010-05-24 13:07 ` Urs Schreiber
2010-05-26 13:48 ` Joyal, André
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