On an enhancement of the category of shifted L-infinity algebras

2014/06/06 by Vasily Dolgushev, Dolgushev, Vasily A., Christopher L. Rogers +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1406.1744

openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a symmetric monoidal category LIE^MC whose objects are shifted L-infinity algebras equipped with a complete descending filtration. Morphisms of this category are "enhanced" infinity morphisms between shifted L-infinity algebras. We prove that any category enriched over LIE^MC can be integrated to a simplicial category whose mapping spaces are Kan complexes. The advantage gained by using enhanced morphisms is that we can see much more of the simplicial world from the L-infinity algebra point of view. We use this construction in a subsequent paper to produce a simplicial model of a (∞,1)-category whose objects are homotopy algebras of a fixed type.

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