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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2023

    have boosted this old entry,

    adding discussion of amalgamated free products

    and some references

    (haven’t found a textbook yet that would admit to the amalgamated case, please add if you have one at hand)

    (interesting to look at the historical references)

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2023

    for completeness, I made more of the underlying category theory notions notationally more explicit

    diff, v7, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeMay 16th 2023

    the article states

    is the corresponding pushout

    G 1 AG 2G 1⨿HG 2GrpG_1 \star_A G_2 \;\; \simeq \;\; G_1 \overset{H}{\amalg} G_2 \;\; \in \; Grp

    (or generally the colimit) in the category Grpd

    surely you mean “in the category Grp”?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2023

    fixed (twice! blame my fingers :-)

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2023

    added sentence cross-linking with direct product of groups

    diff, v8, current