Homotopy composition of cospans
  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. 
Joachim Kock and David I. Spivak
math.CT cs.LO math.AT quant-ph