Re: bilax_monoidal_functors

["Fred E.J. Linton" <fejlinton@usa.net>]

Jeff Egger <jeffegger@yahoo.ca> wrote, in part,

> My objection to the phrase "autonomous category" (which
> Dusko brought up) has less to do with defending Fred
> Linton's original usage of that phrase than the fact
> that "autonomous category" is a special case (and, from
> one point of view, a rather uninteresting special case)
> of "star-autonomous category", whereas it sounds like
> "star-autonomous category" should mean an "autonomous
> category" with some extra structure.  (And, of course,
> this once was the case, w.r.t. the older terminology.)
> This is confusing; hence one term or the other should
> be changed.  I am, in fact, open to all suggestions,
> though I cannot help but prefer that "star-autonomous"
> be kept and "autonomous" changed.

Without seeking to prolong the use of "autonomous" today,
let me just say in my defense that, at the time I brought
that term into use, I was thinking it was the sort of
place-holder name that would, eventually, be replaced (as
it has been) by something more appropriate. This was, as I
recall, also the original motivation for the term "exact";
fortunately for its coiners, "exact" worked so well that
it never did need to get replaced. "Autonomous," on the 
other hand, was not nearly as felicitous a choice, and has
long since been superceded -- I have no qualms about that,
nor any regrets (all the fewer because, as I recall, I was
at that time thinking only of symmetric closed monoidal
categories V for which the Set-valued Hom functor V(E, -) 
(E the monoidal unit object) was faithful :-) ).

Cheers, -- Fred




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