Abstract
If you have a monodial closed category, a notion of "the object of all path components" and an object you are willing to call a circle, you can define the homotopy objects π_n(X). Mike Barr's paper "Building Closed Categories" helps us construct useful examples. In general, there will be a "generic path" and in one of our examples the maps from the generic path to itself are all given by polynomials. Mike Barr, Bob Raphael and I are just starting this work and the talk will mainly explore some examples.