Properadic homotopical calculus
Quantum Algebra
2019-11-26 v2 Category Theory
Abstract
In this paper, we initiate the generalisation of the operadic calculus which governs the properties of homotopy algebras to a properadic calculus which governs the properties of homotopy gebras over a properad. In this first article of a series, we generalise the seminal notion of infini-morphisms and the ubiquitous homotopy transfer theorem. As an application, we recover the homotopy properties of involutive Lie bialgebras developed by Cieliebak--Fukaya--Latschev and we produce new explicit formulas.
Cite
@article{arxiv.1910.05027,
title = {Properadic homotopical calculus},
author = {Eric Hoffbeck and Johan Leray and Bruno Vallette},
journal= {arXiv preprint arXiv:1910.05027},
year = {2019}
}
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