An infinity-groupoid is finitely-presented when it is equivalent to the free infinity-groupoid on a finite family of generators, possibly of different dimensions.


**Is the infinity-groupoid of a finite CW complex finitely-presented?**


It seems to me this question is relevant for homotopy type theory, in which topological spaces are constructed as higher inductive types from a finite family of generators.



Is the infinity-groupoid of a finite CW complex finitely-presented?
A CW structure is precisely a presentation of an $\infty$-groupoid, and so "finite CW complex" means precisely "finitely presented $\infty$-groupoid." 


