We prove that, if a pair of semicosimplicial spaces arises from a colored operad, then the semitotalization has the homotopy type of a relative double loop space and the pair is weakly equivalent to an explicit algebra over the two dimensional Swiss-cheese operad .
"Swiss-cheese action on the totalization of action-operads." Algebr. Geom. Topol. 16 (3) 1683 - 1726, 2016. https://doi.org/10.2140/agt.2016.16.1683