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Aug 9, 2017 at 11:08 comment added Ronnie Brown Yes: in fact they do use the fundamental groupoid on a set of base points.
Aug 8, 2017 at 22:23 comment added Daniel Moskovich The sequel to this paper does use the word "groupoid": arxiv.org/abs/1404.0282
Aug 8, 2017 at 20:34 comment added Ronnie Brown What I do not understand is that the word "groupoid" does not occur in the Habiro-Widmer paper, though they do use the sets of homotopy classes of paths $\pi_1(p,q)$ between two points $p,q$ for certain $p,q$.
Aug 8, 2017 at 6:02 history answered Daniel Moskovich CC BY-SA 3.0