ABSTRACT
Wehave found ourselves in somewild places and spaces and that is fine, as long as we can get home again. To tell the story of the spaces we have seen and the places we have been, we need ways to move from space to space and ways to compare spaces both in terms of the underlying sets and in terms of the operations on the sets. Functions (a.k.a. transformations in linear algebra) are the magic slippers that can take us where we want to go. Of course not every function has magic in its correspondences. Different functions have different properties, and we need to identify those (magical) properties that can carry us home.
