Subject: categories: Re: co-

From: John R Isbell <[email-masked]>
Date: Sat, 4 Jul 1998 11:36:35 -0400 (EDT)

The Shorter OED is doubtless not an infallible
guide to mathematical etymology, but it has
something obvious that we have all been missing
(as far as I have seen yet):

    <2 {\it Math.} Short for {\it complement},
   in the sense 'of the complement' (as 
   {\it cosine}), or 'complement of' (as
   {\it co-latitude}).>

All categorical 'co's are surely that kind. In
prticular, cohomology like cosine. If Steenrod 
had in mind covariant, contravariant, why would 
he say 'cohomology'? Had he said 
'contrahomology' it would be clear. (It is
relevant, I think, that in Lefschetz' first
Colloquium book he called cohomology, such as
$H^1$, homology in negative dimensions, as
$H_{-1}$.)
   Cofinal has to be Latin 'cum'+final.
       John