Homomorphisms of \(L_\infty\) modules (Q2255542)

The notion of Lie algebra admits a homotopy version sometimes defined by replacing the Lie operad by a cofibrant replacement. Explicitly this means that there are higher brackets which verify in particular a generalized form of the Jacobi identity. The subject of this article is to define what a homomorphism of \(L_\infty\)-modules is (over a fixed \(L_\infty\)-algebra \(L\)), in purely computational terms, given by explicit formulas. The guiding principle is the correspondence between Lie module homomorphisms \(M \rightarrow M'\) and Lie algebra homomorphisms \(L \oplus M \rightarrow L \oplus M'\).