meaningful and formalistic names

meaningful and formalistic names

[Marco Grandis]

Dear colleagues,

I apologise for commenting a third time on this point. I think I can
suggest a solution which could solve most of the problems mentioned
in this line (not all of them), and can be used in various similar
situations.

We have a meaningful name for a concept, say involutive category (or
category with involution). This term is even well established in
category theory (see (*) below). Its main drawback is that the
attribute "involutive" is not as flexible as we would like it to be,
in order to develop a theory of such things: an involution-preserving
functor cannot be called an "involutive functor", as Peter Selinger
points out; and so on.

On the other hand, typographical prefixes, like dagger or star, are
already used in the same sense. They are flexible (you can say dagger
category, dagger functor, and so on) and their authors do not want to
give up the terminology of their previous works. Their big drawback -
even forgetting about the fact that "category with involution" is an
old, well established term - is that, being meaningless (or
formalistic, as Walter Tholen prefers to say), nobody would search
for them unless (s)he is already aware of this use. Thus, papers
using such a terminology are often confined to some restricted
domain; and this terminology will be reinvented again and again, with
other acronyms or typographical signs.

The solution I suggest:

One can call such structures with a double name, a meaningful
(possibly well established) name and a flexible one. In the present
case this might be:

- involutive categories (say), alias "prefix"-categories,
- involution-preserving functors (say), alias "prefix"-functors,

where "prefix" stays for the letter or acronym or typographical sign
preferred by the author.

In a title one would only use the meaningful terms, which can be
easily retrieved in a search. In the body of a paper, one would use
both terminologies in the main definitions and the short, adaptable
prefix most of the time.

---

(*) Searching in MathSciNet, under "Anywhere", I find:

- category with involution: 41 items, starting with 1969
- involutive category: 5 items
- dagger category: 0 items  (including variants, like $\dagger$-category
- star category: 1 item  (all variants I can think of give the same
item)

(Of course, various dagger- or star- papers might be not yet on
MathSciNet.)

With best regards

Marco Grandis