Basic sections of LA-groupoids

TL;DR

This paper introduces the concept of basic sections in LA-groupoids with injective core-anchor maps, demonstrating their Morita invariance and offering a simplified model for sections of stacky Lie algebroids.

Contribution

It defines basic sections for a specific class of LA-groupoids and proves their Morita invariance, simplifying the understanding of stacky Lie algebroid sections.

Findings

Basic sections are Morita invariant.

The new model simplifies the study of stacky Lie algebroids.

Equivalence with multiplicative sections established.

Abstract

We define the notion of basic section of an LA-groupoid whose core-anchor map is injective. Such a notion turns out to be Morita invariant, so that it provides a simpler model for the sections of the stacky Lie algebroids presented by such LA-groupoids, yet equivalent to the well-known model provided by their multiplicative sections.