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 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 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: nucleus of a profunctor

Bottom of Page

1 to 6 of 6

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 5th 2014

    I started an entry at nucleus of a profunctor. Much more could be said, including plenty of examples. I don’t know what people think about splitting examples into those where the profunctor is Hom from the rest.

    Do we not already have something on the ’center of an adjunction’, perhaps under a different name?

    We have Legendre transfomation already. Is there a standard way to take the Legendre-Fenchel transform as a generalization?

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 22nd 2014

    I have a conference talk on duality to give in September, hence my looking at the above.

    If at Isbell duality, we have

    Isbell duality is a template for many other space/algebra-dualities in mathematics,

    and this is a special case of the duality formed by this nucleus construction, is there a reason that choosing Hom as the profunctor leads to space/algebra dualities, or should we expect such dualities to arise in non-Hom cases?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2014
    • (edited Aug 22nd 2014)

    I suppose it would be worthwhile to look at more general dualities, but at least one can say of course that Hom is in some way the canonical/archetypical/tautological example and hence somehow special or somehow more fundamental than other examples will be.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 22nd 2014

    But the truth-valued Galois correspondence ones don’t come from Hom, as listed here.

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeJun 9th 2023

    Explain how the two VV-functors in question are constructed.

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeOct 26th 2023

    Added another reference, to Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions.

    diff, v7, current

1 to 6 of 6

  1.