Subject: categories: co-

From: Paul Taylor <[email-masked]>
Date: Mon, 6 Jul 1998 19:15:35 +0100 (BST)

I seem to have started an avalanche.

There seem to be two contradictory theories - maybe someone 
could make the codictory.

1. co- versus nothing, from trigonometry
2. co- versus contra-

I knew the words covariant and contravariant both before I knew anything
about categories, and from a book which predated (sorry, pre-dated)
category theory, namely
	A.S. Eddington's "Mathematical Theory of Relativity" (1925),
which was the only serious maths book I could find in the town library
in High Wycombe (half way between London and Oxford) when I was at
school.  What it was doing there, I can't imagine.

As to "cofinal", I worked out its etymology for myself, but Saunders
Mac Lane (if he was in fact the culprit) could have re-invented its
etymology instead of generating the confusion.  Besides, (co)final
functors are those between diagram-shapes which give rise to the same
colimits, so the prefix seems reasonable to me.

Paul