A cohomological proof for the integrability of strict Lie 2-algebras

TL;DR

This paper establishes a cohomological approach to prove the integrability of strict Lie 2-algebras by relating their cohomologies to those of strict Lie 2-groups through van Est type theorems.

Contribution

It introduces a cohomological proof method for the integrability of strict Lie 2-algebras, providing a new perspective compared to previous approaches.

Findings

Proves van Est type theorems connecting cohomologies of Lie 2-groups and Lie 2-algebras.

Demonstrates the integrability of strict Lie 2-algebras using cohomological techniques.

Provides a novel proof framework for Lie 2-algebra integrability.

Abstract

We prove a series of van Est type theorems relating the cohomologies of strict Lie 2-groups and strict Lie 2-algebras and use them to prove the integrability of Lie 2-algebras anew.