Talk:Grothendieck's relative point of view

misleading use of the term relative?

This may be a borderline article, If this article is in WP then there really should be an article on the Beck-Chevalley condition. An argument for putting it in, is that the term "Grothendieck's relative POV"–a very common phrase–often leads people to expect that it's somehow connected with the use of "relative" in Einstein's Relativity Theory". It is, in a way, since a map X -> S can be thought of as an "aspect"–I just invented this use of the term–of X from S's POV. However, when one calls "X -> S" relative, it is X that one is really interested in, and in fact one names the category, after X. E.g. one might (and often does) say "let X -> S" be a curve, when what one means is that X is a family of curves parametrized by S.

So the use of "relative" here is misleading, but I suppose we're stuck with it. I think a much better term would be "fibrational".--Foobarnix (talk) 14:42, 2 August 2015 (UTC)