Re: Straw man terminology

[Urs Schreiber <urs.schreiber@googlemail.com>]

> I also like Andre's term ``quasi-categories'' and prefer it to the
> infinity alternatives, for the reasons he gives. Like Kan complex,
> it has a fixed and evocative definite meaning, unlikely to be confused
> with anything else.

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.


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