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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2021

    some minimum, to connect to Cayley graph and geometric group theory

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2022

    Added (here) mentioning of the example of the braid group.

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2022
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2023

    I am looking for a HoTT reference which would write out the construction of groups GG generated by

    • a set SS of generators,

    • subject to relations RId ΣS(pt,pt)×Id ΣS(pt,pt)R \;\subset\; Id_{\Sigma S}(pt,pt) \,\times\, Id_{\Sigma S}(pt,pt)


    • the looping of

    • the 1-truncation of

    • the homotopy cofiber of

    • the evident function ((p 1,p 2):RS 1)ΣS\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?