Lie algebroids are curved Lie algebras

Abstract

We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of algebras over a complete operad.

Added a new section with examples and applications. Corrected minor mistakes throughout. Comments are still welcome