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

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 \((\infty,1)\)-category whose objects are homotopy algebras of a fixed type.