Michael Kleber writes << Fred is right that many terms that might apply are overloaded. I like "pull-back" for this notion, and I think it's unambiguous: "the pull-back of G by F" is definitely x |-> F^-1(G(F(x))). On the other hand, people might look at you funny for using it.

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I might agree, except that "pull-back" is already widely used in math for a family of different situations. (For example, if X,Y,Z are sets and Map(A,B) denotes the set of all functions from set A to set B, then given a fixed function f: X -> Y we obtain a function f* : Map(Y,Z) -> Map(X,Z) via f*(g) := f o g for any g in Map(Y,Z). Then f o g is called the pull-back of g by f.) What I know as the totally standard term for F^(-1) o G o F is the "conjugate" of G by F. It has equivalent interpretations as 1) re-expressing G in terms of a new coordinate system as defined by F, and 2) performing the transformation G in "a new place" as defined by F. (E.g., if G is a rotation about the origin of R^2 about the origina, and F is a translation F(v) = v - v_0, then F^(-1) o G o F expresses the equivalent rotation of R^2 about v_0. --Dan --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele