categories: Re: lluf subcategory

["Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

>
> > I've heard the term "lluf subcategory" meaning "subcategory with
> > the same objects but possibly fewer morphisms".   Is there a
> > reference for this usage?
>
> Two references to "lluf subcategories" that I am aware of:
>
> 1. Categories for Types - Roy L. Crole - 1993 - page 49
>
> 2. Practical Foundations of Mathematics - Paul Taylor - 1999 - page 211
>    (where the term "wide subcategory" is suggested as synonym).
>
> And thank you, Paul, for bringing this up, since it reminded me to ask:
>
> Does anyone know the origin of the term "lluf", or how it should be
> pronounced?
>
I've been looking through Peter Freyd's papers, and the earliest
occurrence of "lluf" that I can find is in "Algebraically complete
categories", published in the proceedings of the 1990 Como meeting
(Springer LNM 1488, 1991). It is used there (on page 101) without
comment or explanation, which suggests that Peter must have used it
before, but I can't find an earlier occurrence. A lower bound for
its first occurrence is provided by Peter's paper "Choice and
well-ordering" (Ann. Pure Appl. Logic 35, 1987), where the concept
occurs without being so named.

As regards pronunciation, I've always thought that since it looks
like a Welsh word it should be pronounced as such, i.e.
(approximately) "thleeve". (The Welsh "ll" doesn't correspond to
any sound representable by a combination of consonants in English.)

Peter Johnstone