since atiyah and segal described the notions of topological quantum field theory (tqft) and conformal field theory (cft), mathematicians have been looking for a suitable n-category framework to describe cobordisms with corners and a more general tqft involving such cobordisms as a functor from that higher category of cobordisms with corners to a higher category of vector spaces. the problem deals with such standard difficulties of higher category theory as weak vs. strict axioms, coherence, suitable diagrams, etc.: almost every higher category theorist has this problem in the back of her head, but nobody seems to have gotten through to a satisfactory solution. in the talk, i will describe the set up mark feshbach and i have found.