Transitive Lie algebroids - categorical point of view

TL;DR

This paper explores the classification of transitive Lie algebroids and constructs a classifying space, enabling the description of their characteristic classes through a categorical framework.

Contribution

It introduces a categorical approach to classify transitive Lie algebroids and constructs a classifying space for their characteristic classes.

Findings

Classification framework for transitive Lie algebroids

Construction of a classifying space for these algebroids

Description of characteristic classes via natural transformations

Abstract

The intention of this article is to make an attempt of classification of transitive Lie algebroids and on this basis to construct a classifying space. The realization of the intention allows to describe characteristic classes of transitive Lie algebroids form the point of view a natural transformation of functors similar to the classical abstract characteristic classes for vector bundles.