Re terminology:

[Joyal@mta.ca, Andre <joyal.andre@uqam.ca>]

Dear Urs and Ronnie,

Sergei Soloviev wrote:

>My personal opinion is that this process is very much influenced
>by the pressure of "bibliometry", "impact factors" and other "modern
>trends" - people often not very scrupulously invent and reinvent
>terminology to be better cited, and, conscious or not, it often very
>much smells of imposture.

Urs Schreiber wrote:
 
>It seems to follow the well established terminology in higher category
>theory, which proceeds: category, 2-category, 3-category, ....
>infinity-category and  groupoid, 2-groupoid, 3-groupoid, ...
>infinity-groupoid.


I introduced the terminology "quasi-category" as an alternative name 
for weak Kan complexes because I wanted to suggest that the theory of these objects 
was closer to category theory than to the theory of Kan complexes.
For example, the notion of an initial object in a quasi-category 
is very important, like that of initial object in a category.
But only a contractible Kan complex can have an initial object. 
The theory of quasi-categories turns out to be amazingly close to category theory
despite the fact that its natural setting is simplicial homotopy theory.
The name "quasi-category" is for me less frightening than
"infinity-category" which has the name of God into it.
More seriously, why should we attach the prefix "infinity" to an object 
which is no more endless than the set of natural numbers, or the set of rational numbers, 
or the simplicial category Delta? The terminology could be reflecting the
(relative) failure of the algebraic approach to higher categories.
An algebraic description of homotopy type of the 2-sphere is missing
and it could be endless. But the 2-sphere is easy to describe simplicially: 

   S^2= Delta[2]/partial \Delta[2]


Best, 
André

 


-------- Message d'origine--------
De: categories@mta.ca de la part de soloviev@irit.fr
Date: jeu. 20/05/2010 03:58
À: Ronnie Brown
Objet : categories: Re terminology:
 
My personal opinion is that this process is very much influenced
by the pressure of "bibliometry", "impact factors" and other "modern
trends" - people often not very scrupulously invent and reinvent
terminology to be better cited, and, conscious or not, it often very
much smells of imposture.

Sergei Soloviev


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