Re: "Historical terminology"

[Vaughan Pratt <pratt@cs.stanford.edu>]

JeanBenabou wrote:
> (i) Your "guess" about cartesian closed categories is most certainly
> correct. I knew that Eilenberg/Kelly had explicitly used this name
> in their La Jolla paper, and it is probably the first instance,
> because "closed", in this sense, was first introduced in that paper,
> as far as I know..

What most impressed my students and me two decades ago, when we were
applying the concepts of EK65 to modeling concurrency, was their attempt
to define "closed" as a self-contained notion independently of any
tensor product as its left adjoint (or so it seemed to us).  This
defeated us.  Has a clearer story of that attempt, or any related story,
emerged in the meantime?

> (iii) I agree with you on the idea that the "natural" definition of
> locally  cartesian closed category  should not  imply the existence
> of a terminal  object. If I asked the question, it is because in
> Johnstone's "Elephant" he does assume a terminal  object. Has such an
> assumption become, now, commonly accepted in the definition ?

Hopefully not.  If affine geometry has no origin, why should locally
cartesian closed categories have a global reference point?  (What would
Andy Pitts have decided there, and for that matter the orientation of
profunctors in B2.7, which seems backwards from say Borceux?)

Vaughan