Homotopy morphisms between convolution homotopy Lie algebras

DOI10.4171/JNCG/351zbMath1440.18040arXiv1712.00794MaRDI QIDQ2180248

Felix Wierstra, Daniel Robert-Nicoud

Publication date: 13 May 2020

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1712.00794

zbMATH Keywords

rational homotopy theoryoperadshomotopy algebras

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Loop space machines and operads in algebraic topology (55P48) Homotopical algebra, Quillen model categories, derivators (18N40) Algebraic operads, cooperads, and Koszul duality (18M70)

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