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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 6th 2022
    • (edited Nov 6th 2022)

    A dedicated discussion of the comparison maps between any adjunction and its initial Kleisli- and terminal monadic adjunction is being alluded to in various related entries, but none of them has really been admitting to details or giving any concrete citations.

    This entry is meant to fill that gap. It’s unfortunate that this important concept does not have a more descriptive name. I have added some words of disambiguation in order to account for this.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeApr 4th 2023

    Add some properties.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2023

    Best to give a citation (if not a proof).

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeApr 4th 2023

    I added another link, which hopefully gives enough details to act as a proof sketch.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2023

    Hopefully? :-)

    Just to clarify, I am not asking for myself but for the nLab — I am asking for, say, when in ten years from now a kid happens upon this statement and starts a goose chase on MathOverflow asking random people about how to prove what they will call another one of those unjustified claims on the nLab.

    Best to pre-empt this right when adding the claims.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeApr 30th 2023

    Is there a name in the literature for a right adjoint functor whose comparison functor has a left adjoint? (Somewhat analogous to descent type, which specifies a different property of the comparison functor.)