Homotopy prefactorization algebras (Q6566581)

Some general theory of (pre)factorization algebras can be found in [\textit{K. Costello} and \textit{O. Gwilliam}, Factorization algebras in quantum field theory. Volume 1. Cambridge: Cambridge University Press (2016; Zbl 1377.81004)]. The goal of the paper under review is to show that the (coloured) operad governing prefactorization algebras is the composition of the operad governing cosheaves and the operad governing certain coloured commutative algebras. Both factors are shown to be Koszul operads, while the distributive law between them satisfies the appropriate diamond lemma for the composite also to have the Koszul property. An explicit description of the Koszul dual (and thus of a resolution) is described.