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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2013
    • (edited Nov 16th 2013)

    gave representation theory a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over BG\mathbf{B}G and added the following homotopy type representation theory – table, which I am also including in other relevant entries:

    homotopy type theory representation theory
    pointed connected context BG\mathbf{B}G ∞-group GG
    dependent type ∞-action/∞-representation
    dependent sum along BG*\mathbf{B}G \to \ast coinvariants/homotopy quotient
    context extension along BG*\mathbf{B}G \to \ast trivial representation
    dependent product along BG*\mathbf{B}G \to \ast homotopy invariants/∞-group cohomology
    dependent sum along BGBH\mathbf{B}G \to \mathbf{B}H induced representation
    context extension along BGBH\mathbf{B}G \to \mathbf{B}H
    dependent product along BGBH\mathbf{B}G \to \mathbf{B}H coinduced representation
    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 22nd 2013

    Relevant material happening at the nCafe here.

  1. fixed a very tiny typo: , -> .


    diff, v26, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 19th 2019
    • (edited Jan 19th 2019)

    added pointer to

    • Klaus Lux, Herbert Pahlings, Representations of groups – A computational approach, Cambridge University Press 2010 (author page, publisher page)

    diff, v27, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2021

    added pointer to:

    diff, v33, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 28th 2022
    • (edited Jan 28th 2022)

    for when the editing functionality is back: the entry representation theory should have a pointer to:

  2. added textbook


    diff, v37, current

    • CommentRowNumber8.
    • CommentAuthorAli Caglayan
    • CommentTimeMay 24th 2024

    What is the relation with “representation theory in HoTT” and representation theory? I’m sure I could work out the details if I sat down, but reading the article it doesn’t really give a clear link. It would be good if that section was linked back with better understood concepts.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 24th 2024

    What do you understand by “representation theory”? The standard theory of group actions on vector spaces? One would think linear HoTT best suited for that.

    • CommentRowNumber10.
    • CommentAuthorAli Caglayan
    • CommentTimeMay 24th 2024

    Right, what you would usually learn in a first course on representation theory. How exactly does linear HoTT help here? My understanding is that linear HoTT comes from linear logic. Is there a connection there to linear algebra?

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2024

    Yes. For exposition try from slide 16 on here (view in full-screen mode) or the discussion here.

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 10th 2024

    added pointer to:

    diff, v39, current