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nLab > Latest Changes: plethory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorJoe Moeller
    • CommentTimeJun 11th 2021

    Added a reference to Tall–Wraith. Changed ∘:P⊗ kP→P\circ: P \otimes_k P \to P to ∘:P⊙ kP→P\circ: P \odot_k P \to P. Added redirects.

    diff, v3, current

    • CommentRowNumber2.
    • CommentAuthorJoe Moeller
    • CommentTimeJun 11th 2021

    Added related concepts section. Added reference to paper “Schur functors and categorified plethysm”.

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeJun 11th 2021
    • (edited Jun 11th 2021)

    Good to see Dave and Gavin’s paper being mentioned. I had forgotten about it. (Dave Tall was at that time my PhD supervisor, and choir master! I had had both as lecturers in my UG years.)

    • CommentRowNumber4.
    • CommentAuthorJoe Moeller
    • CommentTimeJun 11th 2021

    Added an idea section. Added a definition section which includes the slightly simpler definition found in Tall–Wraith.

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 14th 2021

    Added something on its derivation from plethysm.

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTime3 days ago

    Is there a reason this page is distinct from Tall–Wraith monoid? It seems to describe the same concept.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTime2 days ago

    Just to check: With your other suggestion (there) to merge bimodel with Tall-Wraith monoid, you actually want to merge all three entries

    1. Tall-Wraith monoid

    2. bimodel

    3. plethory

    ?

    I don’t know about any of these entries, ideally their authors would chime in.

    However, the repeated question for “is there a reason” for why things on the nLab are how they are is unlikely to lead very far, I am afraid: Things here rarely develop according to a masterplan.

    Instead, to move this forward it would probably help if you list your reasons for why to merge certain entries, and if after some while there is no opposition and you feel you know what you are doing, then just go ahead and do it.

  8. There is also the idea of concept with an attitude to consider if these concepts are the same but arose in different settings.

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTime2 days ago
    • (edited 2 days ago)

    The level of generality is not the same. So better they stay separated.

    According to the page biring,

    Birings form a monoidal category thanks to the fact that functors of this form are closed under composition. A monoid object in this monoidal category is called a plethory. A plethory is an example of a Tall–Wraith monoid.

    • CommentRowNumber10.
    • CommentAuthorvarkor
    • CommentTime2 days ago

    In the paper Schur functors and categorified plethysm referenced on this page, they use “plethory” in the generalised sense, and use “ring-plethory” for this specific case, which seems reasonable.

1 to 10 of 10

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