JournalsjncgVol. 13, No. 4pp. 1463–1520

Homotopy morphisms between convolution homotopy Lie algebras

  • Daniel Robert-Nicoud

    Zürich, Switzerland
  • Felix Wierstra

    Université Sorbonne Paris Nord, France and Stockholm University, Sweden
Homotopy morphisms between convolution homotopy Lie algebras cover
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Abstract

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 \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.

Cite this article

Daniel Robert-Nicoud, Felix Wierstra, Homotopy morphisms between convolution homotopy Lie algebras. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1463–1520

DOI 10.4171/JNCG/351