Re: autonomous terminology: WAS: bilax monoidal functors

Re: autonomous terminology: WAS: bilax monoidal functors

[Dusko Pavlovic]

thanks for the suggestions about the autonomous terminology. i think i got
an idea for a minimally invasive solution.

we probably shouldn't go too deep into the general questions, but colin
mclarty's cryptic comment is very interesting to me, and it seems to
strike at the heart of some matters of interest.

On May 9, 2010, at 3:41 PM, Colin McLarty wrote:

> Dusko Pavlovic Asks
>
>> is there any reason why words should be taken seriously?
>
> That just depends on whether or not you want to be understood by
> people who do not already know everything you are going to say.

there are at least two ways to interpret this.

1) "you can only say something new if you declare what your words mean.
otherwise, people will interpret them in their own way, and understand
only what they already know." --- this is what my sociology teacher would
say.

2) "you can only say something new if you contribute to the evolution of
language. otherwise, everything you say are just words that people already
know, mostly in combinations that they already tried." --- this is what my
poetry teacher would say.

i am not sure whether you meant (1) or (2), colin. maybe you tried to say
something that i don't know already :) in any case, i suspect that many
people here would tend to disagree with my poetry teacher.

but the distinction between (1) and (2) stretches beyond my high school
teachers. eg, hilbert would surely subscribe something like (1). all those
monolithic foundations and logics and set theories can be viewed as
efforts to clearly define the words that we use in math.

categories, on the other hand, were proposed as a tool for the *working*
mathematician. people cared that category theory was a dynamic language,
with its philosophical roots in *dialectics*... not that we didn't define
our terminology; but categorical work was more about capturing conceptual
flows by adjunctions, and the flows of equations by arrows, than about
carving words in stone.

nowadays, the distinction between (1) and (2) has become very concrete.
language is processed on the web, and the problem that the meaning of data
is not clearly defined or structured has became a technical problem. two
strategies were proposed:

1) semantic web: let us standardize ontologies, anotate data
syntactically, and contribute them to the global library;

2) search: follow the hyperlinks and extract the meaning of data
dynamically, by analyzing their distribution on the network. eg, if one
web site links to another web site, then it lends it some of its
reputation, and some of its meaning.

paradigm (1) has generated a lot of interesting research. people defined
very precise very carefully classified families of terms in very large
ontologies. recently, some of them were even populated by data.

paradigm (2) works. it changed every science, and made possible a couple
of new ones. if there is a question of terminology, ask google. show me
200 papers about motivic cohomology, sorted by popularity. what is motivic
cohomology? long live dialectics. things shouldn't be taken seriously only
because of a shortage of humor in the world.

all the best,
-- dusko

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

Re: autonomous terminology: WAS: bilax monoidal functors

[Jeff Egger]

Hi Dusko,

> i am reluctant call them dagger star autonomous categories,
> because it is a mouthful.

Perhaps it's a symptom of growing up in a country where
"Kangiqsualujjuaq" is considered a perfectly acceptable
name for a village, but I don't think that "dagger star-
autonomous" is a mouthful.  It's only one syllable longer
than "sesquipedalian", and one less than "linearly
distributive", neither of which I would hesitate to use
in day-to-day conversation, should the occasion arise.

It even scans nicely.

Moreover, it communicates something (at least to me); for
better or worse, both "dagger" and "star-autonomous" are
both established terms, and I can see how they might be
combined.  Agglutination, though often mocked, is often
effective.

> 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?

One of the many curious features of the English language is
that adjectives are never inflected; assuming you use TeX,
why not take advantage of this fact in your source code?
\def\dsa{dagger star-autonomous}

> peter suggests DSA-categories.

If you're publishing in a print journal, or a conference
proceedings with a hard page-limit, then that seems sensible
(though I'd drop the hyphen).  Otherwise, do us all a favour
and stick to the long form: pixels are cheap, as editors of
TAC are wont to say.

> (maybe someone will abbreviate them to D-categories...)

What's the point of that?  D-category could stand for (just
plain old) dagger category, or differential category, or any
number of other things.  But maybe someone some day will
\def\dsa{Pavlovic}.

Cheers,
Jeff.





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

Re: autonomous terminology: WAS: bilax monoidal functors

[posina]

> is there any reason why words should be taken seriously?

I'd take words seriously for the simple reason that they are an expression
of concepts with which we reason. I hope that this line of questioning is
not indicative of the future behind us: treating the notion of GRAMMAR
lightly (as in replacing grammar with look-up tables), which is a sign of  a
failure to distinguish between the concepts of PARTICULAR and GENERAL
(contexuality does not rationalize confusing GENERAL with PARTICULARS). The
distinction between GENERAL and PARTICULAR is an inheritance that I am most
proud of and thankful for.

Thank you,
posina


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

Re: autonomous terminology: WAS: bilax monoidal functors

[Colin McLarty]

2010/5/9 Dusko Pavlovic <Dusko.Pavlovic@comlab.ox.ac.uk>:

Asks

> is there any reason why words should be taken seriously?

That just depends on whether or not you want to be understood by
people who do not already know everything you are going to say.

best, Colin


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

autonomous terminology: WAS: bilax monoidal functors

[Dusko Pavlovic]

> 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?


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