Homotopy morphisms between convolution homotopy Lie algebras

Abstract

In previous works by the authors, 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 $\infty$-morphism between (co)algebras over a (co)operad associated to a twisting morphism, and show that this bifunctor can be extended to take such $\infty$-morphisms in either one of its two slots. We also provide a counterexample proving that it cannot be coherently extended to accept $\infty$-morphisms in both slots simultaneously. We apply this theory to rational models for mapping spaces.

37 pages; v2: minor typo corrections, updated bibliography, final version

Cited by in corpus (2)

• Convolution algebras and the deformation theory of infinity-morphisms
• $E_n$-Hopf invariants