Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: plethory

Bottom of Page

1 to 10 of 10

  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
    • CommentTimeOct 14th 2024

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

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2024

    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.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 15th 2024

    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
    • CommentTimeOct 15th 2024
    • (edited Oct 15th 2024)

    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
    • CommentTimeOct 15th 2024

    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

  1.