# Comparison of spaces associated to DGLA via higher holonomy

## TL;DR

This paper establishes an explicit equivalence between two mathematical structures related to DGLA, using non-abelian multiplicative integration, advancing understanding of higher holonomy in differential graded Lie algebras.

## Contribution

It constructs an explicit equivalence between the nerve of the Deligne 2-groupoid and a simplicial set of differential forms for certain nilpotent DGLAs, utilizing non-abelian multiplicative integration.

## Key findings

- Established an explicit equivalence between the nerve of the Deligne 2-groupoid and differential form simplicial sets.
- Applied non-abelian multiplicative integration to DGLA in the context of higher holonomy.
- Enhanced the understanding of the relationship between DGLA structures and higher categorical models.

## Abstract

Fof a nilpotent differential graded Lie algebra whose components vanish in degrees below -1 we construct an explicit equivalence between the nerve of the Deligne 2-groupoid and the simplicial set of differential forms with values in the Lie algebra introduced by V.Hinich. The construction uses the theory of non-abelian multiplicative integration.