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arXiv · 1910.05027

Properadic homotopical calculus

Eric Hoffbeck·Johan Leray·Bruno Vallette
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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.

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Eric Hoffbeck, Johan Leray, Bruno Vallette. 2019-11-25. Properadic homotopical calculus. https://arxiv.org/abs/1910.05027

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