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nLab > Latest Changes: cohomology in homotopy type theory

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  1. copying article from HoTT wiki

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2022
    • (edited Jun 9th 2022)

    In the Idea-section the line

    Ordinary cohomology denotes cohomology groups with coefficients in ℤ\mathbb{Z}

    is misleading, making it sound like cohomology with coefficients in, say ℚ\mathbb{Q} would not be “ordinary”.

    (The definition that follows is correct, but this lead-in should be reworded somehow.)

    Incidentally, this entry might better be named “ordinary cohomology in…”

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 15th 2022

    added pointer to:

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 15th 2022

    am renaming this page to “ordinary cohomology in …” in order to leave room for things to come

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 15th 2022
    • (edited Jun 15th 2022)

    regarding my comment in #2:

    I have deleted that whole sentence now:

    Ordinary cohomology denotes cohomology groups with coefficients in ℤ\mathbb{Z} this is usually difficult to compute for most spaces, so they are usually broken up into groups for each prime pp with coefficients in ℤ p\mathbb{Z}_p. These can be glued back together via the universal coefficient theorem.

    Even after fixing the sentence, it would be out of place here. If anyone feels this sentence needs to survive, please add a corresponding paragraph to ordinary cohomology and take note that the entry fracture theorem exists.

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2023

    I have brushed-up the list of references (here):

    apart from completing the bib-data, fixing links, and bringing it into chronological order,

    I have added remarks on what each reference is actually about.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorperezl.alonso
    • CommentTimeApr 25th 2023

    Pointer to implementation of cohomology rings in cubical agda: * Thomas Lamiaux, Axel Ljungström, Anders Mörtberg, _Computing Cohomology Rings in Cubical Agda _ ([arxiv:2212.04182] (https://arxiv.org/abs/2212.04182))

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2023

    Thanks! I have added the publication data and the doi-link.

    diff, v6, current

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