The question is as in the title.

(What are some of the) are there any applications of Homotopical algebra (in the context of Quillen’s book “Homotopical algebra”) in better understanding (or developing new theory) of Lie groupoids?

The question is as in the title.

(What are some of the) are there any applications of Homotopical algebra (in the context of Quillen’s book “Homotopical algebra”) in better understanding (or developing new theory) of Lie groupoids?

I am reading Homotopical algebra hoping that this would help me to learn some $\infty$-category theory. Other than that, I do not have any plan. As I am familiar with Lie groupoids, I wanted to see if there is a place where these two interact in a nice way.

(As of now), I do not have any better explanation than this to ask the question.