A model structure on relative dg-Lie algebroids

TL;DR

This paper establishes a model structure on the category of dg-Lie algebroids over certain graded algebras, facilitating future research in derived deformation theory and coisotropic structures.

Contribution

It proves the existence of a model structure on dg-Lie algebroids over non-positively graded commutative algebras, enabling advanced derived geometric studies.

Findings

Model structure existence proven for dg-Lie algebroids

Facilitates future derived deformation theory applications

Supports development of derived coisotropic structures

Abstract

In this Note, for the future purposes of relative formal derived deformation theory and of derived coisotropic structures, we prove the existence of a model structure on the category of dg-Lie algebroids over a cochain differential non-positively graded commutative algebra over a commutative base ring k of characteristic 0.