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

Abstract

We construct a symmetric monoidal category $LI{E}^{MC}$ 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 $LI{E}^{MC}$ 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.

The final version will appear in "Applied Categorical Structures"

References in corpus (2)

• Hydrodynamic Limit For An Active Exclusion Process
• Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group

Cited by in corpus (5)

• A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras
• Action of derived automorphisms on infinity-morphisms
• Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group
• A Variation of the Goldman-Millson Theorem for Filtered $L_{\infty }$ Algebras
• Towards deformation quantization over a Z-graded base