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 deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 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 sheaves 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: Frobenius functor

Bottom of Page

1 to 4 of 4

  1.  
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeApr 26th 2023

    Cross reference ambidextrous adjunction.

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 10th 2023
    • (edited Aug 10th 2023)

    Where it said

    There is no relation to the notion of Frobenius monoidal functor,

    I added

    but there is a close relation to Frobenius monads.

    Which highlights that this entry should be merged with ambidextrous adjunction, either way.

    I realize now that “Frobenius functor” is (much) earlier terminology (though maybe less suggestive than “ambidextrous adjunction”?).

    On the other hand, it seems that people who say “Frobenius functor” base their discussion on Morita 1965 who actually used yet another term, namely “strongly adjoint pair”.

    Given this situation, I am inclined to merge everything into the entry ambidextrous adjunction. What do you think?

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 10th 2023

    Re #2: as an aside, I’m often leery of claims that assert (emphatically!) that there is no relation between two concepts. (I want to ask the author: have you looked deeply into the matter? How can you be so sure?)

    Something like this came up around here, where there was an assertion of “no relation” between Frobenius conditions (a la Frobenius monoids) and Frobenius reciprocity, but after investigation it emerged that there was a relatively close connection. It wouldn’t surprise me all that much if the same were true here.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 11th 2023

    The intent was to say that the terminology is independent: The definition of “Frobenius monoidal functors” is not “monoidal Frobenius functor”.

    I have expanded the remark a fair bit (here)

    also added the original reference for the terminology “Frobenius functor”:

    diff, v6, current

1 to 4 of 4

  1.