On Sun, 26 Sep 2010, Todd Trimble wrote in part:
A case in point is the (I think tongue-in-cheek) expression "fascist functor". Some of you may recall that a "free functor" is to the "left" (in an adjoint string), so a "fascist functor" would be to the "right" in an adjoint string. It's a little jokey (as some people think "evil" is), and yet it still excites emotions, as we discovered in a recent nForum discussion. Something of those reactions were hinted at in the Lab, and I think we would do well to do the same with regard to "evil".
Tongue-in-cheek, indeed: but it goes back a long way. In his 1950 paper "Duality for groups", Saunders Mac Lane used the term "free object" for what we now call a projective object, and (in a footnote) suggested "fascist" for the dual notion (i.e. that of injective object). Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]