Re: Cartesian closed without products

["Ronnie" <ronnie.profbrown@btinternet.com>]

Toby Bartels wrote:

>
> OTOH, the version without unit probably has some use,
> just as non-monoid semigroups occasionally do.

Just a thought that this interest may be more than occasional:
inverse semigroups are closely related to pseudogroups and so are part of
Charles Ehresmann local-to-global view and interests, with a deep relation
to ordered groupoids (see further work by Mark Lawson). So all these partial
units express something on the *local* structure, even if there is a global
unit.  My paper with Aof (based on ideas of Pradines) uses an inverse
semigroup generated by continuous local admissible sections.
(with M. E.-S. A.-F. AOF), ``The holonomy groupoid of a
locally  topological groupoid'', {\em Top. and its  Appl.}, 47 (1992)
97-113.

Is this a rash view that one should look more at inverse categories?

Ronnie Brown