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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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.
    • CommentAuthortimhosgood
    • CommentTimeJul 14th 2019

    created the page for Mealy morphisms and just put in one reference

    Tim Hosgood

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 15th 2019

    Added doi link to paper and clarified etymology.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorRichard Williamson
    • CommentTimeJul 17th 2019
    • (edited Jul 17th 2019)

    Removed the ’not for the adjective mealy’, as I felt it to be unnecessary and jar a bit!

    Also changed the page name to the singular.

    There is lots more that can be added to this page, e.g. how a Meely morphism determines a profunctor, a precise definition, a precise characterisation of when a profunctor determines a Meely morphism, etc. (As discussed in #21 and following here, the page is not quite correct at the moment.)

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 17th 2019

    My immediate thought on reading the page was that in fine category theory tradition (cf prone, supine, wavy, etc) someone had decided to talk about mealy morphisms, and capitalised the word as a stylistic thing. But i guess the page doesn’t need both ’named for this guy Mealy’ and ’but not this other thing’ warnings.

  1. But i guess the page doesn’t need both ’named for this guy Mealy’ and ’but not this other thing’ warnings.

    Yes, exactly, we do not need both I think, but very good to clarify the etymology by including the first one :-).

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJul 18th 2019

    Actually, I thought they were named after Mealy machines. (Which in turn were named after George Mealy, but there’s an extra step in the chain.)

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 18th 2019

    Well, that’s true, I suppose.

    • CommentRowNumber8.
    • CommentAuthorTim_Porter
    • CommentTimeJul 18th 2019

    Added slides by Bryce Clarke from ct2019

    diff, v5, current

    • CommentRowNumber9.
    • CommentAuthorBryceClarke
    • CommentTimeJul 6th 2021

    Added some more references. In particular, I’ve made a note mentioning that Mealy morphisms are the same as “two-dimensional partial maps” due to Lawvere, however I cannot find an original reference for this statement. Street and Lack mention the reference

    • F. W. Lawvere, Closed Categories, Lecture Series at Mathematisk Institut, Aarhus Universitet, February 1971.

    but I don’t suppose there are any written notes from this lecture series.

    In the future I will add an actual definition of Mealy morphism and continue to expand the page.

    diff, v8, current

    • CommentRowNumber10.
    • CommentAuthorBryceClarke
    • CommentTimeFeb 18th 2023

    Added the definition of Mealy morphism between enriched categories from the Paré paper.

    I also removed some references to works of mine, where I refer to something as an example of a Mealy morphism that does not satisfy an additional constraint in the Pare paper that a certain functor be objectwise constant on fibres.

    I will come back later to write a more accurate Idea section for this page.

    diff, v11, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2023

    added:

    floating context menu

    and hyperlinks to a bunch of technical term

    diff, v13, current

    • CommentRowNumber12.
    • CommentAuthorvarkor
    • CommentTimeJan 10th 2024

    Mention the relationship to copowers and the bicategory of profunctors.

    diff, v14, current