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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    for completeness, with pointer to

    • Alexander Grothendieck et al., 16.5.15 in: Éléments de géométrie algébrique IV_4. Étude locale des schémas et des morphismes de schémas (Quatrième partie) Inst. Hautes Études Sci. Publ. Math. 32 (1967), 5–361. Ch.IV.§16–21 (numdam:PMIHES_1967__32__5_0)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added pointer to:

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added Grothendieck’s alternative “formally principal homogeneous space”

    Also added pointer to pages 73-74 in

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added pointer to

    which already has the term “formally principal” on p. 15 (without the “homogeneous”)

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 16th 2021

    So I guess the category of pseudotorsors for GG is (equivalent to) the result of adding a formal initial object to the groupoid BG\mathbf{B}G?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    It’s that trivial only internal to Sets, but the point of the exercise is that it’s much more interesting when internalized in richer ambient categories. Such as schemes. Or G-spaces. Or G-schemes….

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added one more source for the terminology “formally principal homogeneous”:

    diff, v3, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2021

    cross-linked with empty heap

    diff, v4, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 26th 2021

    Made explicit (here) the observation that a pseudo-principal bundle PXP \to X is an effective epi iff it is the GG-quotient projection.

    diff, v7, current

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