Homotopy composition of cospans
arXiv:1602.08739 · doi:10.1142/S0219199716500474
Abstract
It is well known that the category of finite sets and cospans, composed by pushout, contains the universal {\em special} commutative Frobenius algebra. In this note we observe that the same construction yields also general commutative Frobenius algebras, if just the pushouts are changed to homotopy pushouts.
4 pages. In this version: A more direct introduction and a additional few details on the tubular neighborhood argument. Final version, to appear in Commun. Contemp. Math