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some minimum, to connect to Cayley graph and geometric group theory
added pointer to:
I am looking for a HoTT reference which would write out the construction of groups $G$ generated by
a set $S$ of generators,
subject to relations $R \;\subset\; Id_{\Sigma S}(pt,pt) \,\times\, Id_{\Sigma S}(pt,pt)$
as
the looping of
the 1-truncation of
the homotopy cofiber of
the evident function $\Big(\underset{(p_1, p_2) \colon R}{\sum} \, S^1\Big) \longrightarrow \Sigma S$
When I first scanned over Bezem et al.’s Symmetry a while back my impression was that something like that must be what they write down, but now that I have a closer look it seems that they don’t quite get around to. (?) Does anyone else write out group generation using just 1-HITs – in citable form?
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