Re: Straw man terminology

["Joyal, André" <joyal.andre@uqam.ca>]

Dear Urs,

You wrote:

>The term "(infinity,1)-category" is not so much meant as an
>alternative for "quasi-category", but as a intentionally less specific
>term that subsumes concepts that are different from, but equivalent
>to, quasi-categories. Such as Kan-complex-enriched categories or
>complete Segal spaces, or algebraic quasi-categories, or categories
>with weak equivalences, or...

>When doing abstract higher category theory it is useful to be able to
>speak, for instance, of the (infinity,1)-category of all small
>infinity-groupoids and its abstract properties, without having to
>specifically fix a concrete model in terms of which this entity may be
>brought to paper.

I agree that the terminology (infinity,1)-terminology can be useful.
Can I point out that Lurie is calling a quasi-category an infinity-category?
There is a clash of terminology.


Best,
André




[For admin and other information see: http://www.mta.ca/~cat-dist/ ]