Re: co-

[John R Isbell <ji2@ACSU.Buffalo.EDU>]

On Fri, 3 Jul 1998, Paul Taylor wrote:

> What are the origins of the   co-   prefix, as in coproduct, coequaliser ...,
> and who established their use?
> 
> Has anybody ever thought through and written down any guidelines on
> which of a pair of dual concepts is co-?
> 
> Who is reponsible for dropping this prefix from cofinal?
> (A mistake, IMHO).
> 
> Paul
> 
      Fragments: (1) Origin, I don't know, but surely cohomology
  is where it started. The term was used very early, 1937 I think,
  by Norman Steenrod in a paper mainly on universal coefficient
  theorems.
                  (2) The idea of putting forward some such
  guidelines was seriously discussed at La Jolla 1965, and I 
  should say that Sammy Eilenberg killed it single-handed. His
  main point was that anything we Americans might propose would
  be absolutely unacceptable in Paris. Verdier was the only
  Frenchman present; he was well thought of but very young.
                  (1 bis) Of course not covariant-contravariant.
                  (3) I'm not sure what "A mistake IMHO" means.
  Of course, the "co" in cofinal is genetically "con" of
  congress, concatenation. I don't have nice illustrations of
  antecedents of co-homology but it is not 'together' like in
  congress & concatenation. But it is dropped in categorical
  contexts because it is a distracting "co".
      John Isbell