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Properadic homotopical calculus

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arxiv 1910.05027 v2 pith:3NVMXXY3 submitted 2019-10-11 math.QA math.CT

Eric Hoffbeck , Johan Leray , Bruno Vallette This is my paper · ORCID
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keywords homotopycalculuspropertiesgovernsproperadicalgebrasapplicationarticle
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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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  1. Obstruction sequences to homotopy equivalences

    math.AT 2025-09 conditional novelty 6.0 of 10

    Gauge-theoretic obstruction sequences characterize homotopy equivalences between algebras over properads and colored operads, with applications to minimal models over general fields and in etale cohomology.

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