Homotopy composition of cospans

Joachim Kock, David I. Spivak
2017 Communications in Contemporary Mathematics  
It is well known that the category of finite sets and cospans, composed by pushout, contains the universal 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.
doi:10.1142/s0219199716500474 fatcat:ldhjtuy2fjaixfzjrhkybmsko4