13 Dec
2000
13 Dec
'00
1:17 a.m.
Jean Benabou writes:
I am confronted with problems of "contradictory terminology" which I would like to solve and, since english is not my language, I need some suggestions. Let F: Y-----> X be a functor such that for every object x of X the comma category (x,F) is connected.Such functors, although they are not defined in all generality, are called "cofinal" in SGA 4 , and "initial" in Borceux's handbook (Vol.1-§2.11-p.69) but none of these terms is satisfactory.
Mac Lane calls such functors ``final'' in Categories for the Working Mathematician. I do too. Steve Lack.