In previous works by the authors – [26, 31] – a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a homotopy Lie algebra structure. We build on this result by using a more general notion of -morphism between (co)algebras over a (co)operad associated to a twisting morphism, and show that this bifunctor can be extended to take such -morphisms in either one of its two slots. We also provide a counterexample proving that it cannot be coherently extended to accept -morphisms in both slots simultaneously. We apply this theory to rational models for mapping spaces.
Cite this article
Daniel Robert-Nicoud, Felix Wierstra, Homotopy morphisms between convolution homotopy Lie algebras. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1463–1520DOI 10.4171/JNCG/351