Re terminology:

[soloviev@irit.fr]

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



> Peter Sellinger writes recently:
>
> ---------------------------------------------------
>
> I think this is a very apt illustration of what happens if a term with
> an existing meaning is redefined to mean something else. Henceforth it
> is impossible for anybody to use the term (with either meaning)
> without first giving a definition.
>
> ---------------------------------------------------
>
> I completely agree. My own problem is with term `infinity groupoid' which
> is used to describe something which is not even a groupoid, and whose use
> seems to me to militate against the understanding of what has been
> achieved with the original and much earlier definition. I once asked
> Gian-Carl Rota about such change of terminology, in connection with a
> refereeing job, and he agreed that mathematicians are used to creating
> confusion in this way.
>
> There are two easy tendencies: one is to use an old name in a quite
> different way, and the other is to use a new name for an old idea, so that
> the  use of the old term looks old fashioned, and a lot of work may be
> consigned to the dustbin of history, becoming not easy of access  for new
> students.
>
> It seems to be an example of these confusions is the way the simplicial
> singular complex of a space is called an infinity-groupoid, even the
> `fundamental infinity groupoid', when what seems to be referred to is that
> it is a Kan complex, i.e. satisfies the Kan extension condition, studied
> since 1955. The new term sounds like `dressing up' an old idea to look
> new. My personal objection to this change of terminology (i.e. axe to
> grind!) is that this distracts from studying the not so simple proofs that
> strict  higher homotopical structures exist, which mainly are for
> structured spaces (in particular filtered spaces (Brown/Higgins, Ashley),
> n-cubes of spaces (Loday), and more recently smooth spaces (Faria
> Martins/Picken)). The analysis and comparison of these uses should be
> made. It was certainly a relief to Philip and I that we could do something
> with filtered spaces which we could not do for the absolute case; the
> significance of the fact  that these constructions work and lead to
> specific calculations should be thought about.
>
> The term `higher dimensional group theory' which was published in a paper
> with that title in 1982 was intended to suggest developing higher groupoid
> theory and its relations to homotopy theory in the spirit of group theory,
> which meant specific constructions relevant to geometry and calculations,
> even computer calculations,  of many examples, in which actual numbers
> arise as a test of and examples of the general theory, and in which some
> aspects of group theory are sensibly seen as better represented in the
> higher dimensional theory; and example of this is the nonabelian tensor
> product of groups, where group theorists have found lots of pickings.
>
> I am not sure how these terminological problems will be resolved, and I
> know the term (\infty,n)-groupoid has been well used recently but the
> problem of relation to the older ideas, which have had a certain success,
> should be recognised.
>
> Ronnie Brown
>

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