I gave some motivation for my work with Mike Johnson. Our first idea is that one should study paths first and then homotopy. (Following Lavwere) we begin with a topos E. We expect that paths in an object X should have a co-category structure (paths of all dimensions). The first axiom should be that paths are represented. In examples (Sets, simplicial sets, etc.) we find that paths are in fact represented by a family of objects I -> N . The paper we are currently completing deals with the dif- ficult task of defining paths (of all dimensions) in a simplicial set and establishing the -category structure on the paths.