On (Co-)morphisms of Lie Pseudoalgebras and Groupoids

TL;DR

This paper unifies the understanding of morphisms and comorphisms of Lie pseudoalgebras, Lie algebroids, and groupoids by introducing the concept of the $-sum, showing their structural similarities.

Contribution

It introduces the $-sum as a unifying framework for morphisms and comorphisms across Lie pseudoalgebras, algebroids, and groupoids.

Findings

Both morphisms and comorphisms are subalgebras of the $-sum

Unified descriptions for Lie algebroids and groupoids

Structural similarities across different Lie structures

Abstract

We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the $\psi$-sum. We also provide similar descriptions for morphisms and comorphisms of Lie algebroids and groupoids.