Re: omega-cats

two good questions the division into two pieces is relevant to trying to change the geometry into non-abelian cohomology - the boundary as a difference have been looking at some related questions that come up in quasi-bialgebras at the homotopy level, I always have inverses (up to homotopy) - just run the parameter backwards but work in quasi-bialgebra AND in string field theory both suggest imposing stricter inverses e.g. take the category of paths in a space X with endpoint joining of paths as compositions mod out by the relation fg = Id_x and gf=I_y where g is a path from x to y and f is its parameter reverse jim