autonomous terminology: WAS: bilax monoidal functors

[Dusko Pavlovic <Dusko.Pavlovic@comlab.ox.ac.uk>]

> By the way: I don't remember anyone on this mailing list ever asking if
> their own terminology is good.  I only remember them complaining about other
> people's terminology.  I applaud your departure from this unpleasant
> tradition!

to support this departure, i have a terminology question.

last couple of years *dagger monoidal* and *dagger compact* categories
came to be popular. in a recent paper i encountered lots of star
autonomous categories with an additional dagger structure.

i am reluctant call them dagger star autonomous categories, because it is
a mouthful. moreover it seems that listing the operations of a signature
in its name is a bad naming strategy. trying to maintain descriptive names
is a lost cause. linguists have known that languages are not descriptive
since XIX century. mathematicians since much earlier, even since they
started calling everything x and y. we never try to give cars or people
descriptive names, only mathematical structures. a new chemical element is
given an ugly descriptive name only until a simpler one is agreed upon.

i was going to call them *dagger autonomous* but peter selinger pointed
out that this is confusing. indeed, the term *autonomous* has established
a confusing tradition all on its own:

* i believe that fred linton introduced it in the 60s for what would now
probably be called *closed* structure

* barr followed linton's usage with his star autonomous categories. there
are 10s of 1000s of papers using this terminology (eg from the linear
logic times).

* on the other hand, joyal and street called autonomous those categories
where every object has a monoidal dual. that terminology also caught on.

so now, what should we call those "dagger star autonomous categories" if
we don't want to type 30 characters each time we mention them?

peter suggests DSA-categories. (maybe someone will abbreviate them to
D-categories...)

help appreciated.

-- dusko

PS maybe we should rename dagger monoidal to pink monoidal, and star
autonomous to floyd, so dagger star autonomous categories would be pink
floyd categories.

is there any reason why words should be taken seriously?


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