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: retrofunctor

Bottom of Page

1 to 11 of 11

  1.  
    • CommentRowNumber1.
    • CommentAuthorBryceClarke
    • CommentTimeOct 1st 2020

    Created a stub for cofunctor? with some references.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 2nd 2020

    BTW congrats on your paper!

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2020

    I suggest to include author names in double square brackets only if the author page exists or if you create it right away. Because otherwise the links will just remain broken forever and look bad.

    Here Mackenzie’s page did exist, and I added the redirect to it which makes the requested link work here.

    For the last reference I removed the double square brackets on the author names. But feel invited to add them back in – together with the respective author pages.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorBryceClarke
    • CommentTimeJul 3rd 2021

    Added in definition of cofunctor, attempting to mimic to external definition of functor. The use of φ 0\varphi_{0} and φ 1\varphi_{1} feels a bit clunky, so there may be a more appropriate choice of notation.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorBryceClarke
    • CommentTimeJul 3rd 2021

    Made minor changes to definition, added Tikz diagram as a visual aid. Added definition of composition of cofunctors, and noted that small categories and cofunctors form a category. Added several basic examples. I also added a couple of references to my own papers on cofunctors.

    I’d like to make a note somewhere there there are two different conventions in the literature for the direction of a cofunctor. Specifically, this page uses the convention that cofunctors are defined in the same direction as the object assignment, whereas other references (in particular Aguiar 1997, Definition 4.2.1 where cofunctors were first defined) define cofunctors in the direction of the morphism assignment. Where would the most appropriate place to put this note?

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorBryceClarke
    • CommentTimeJul 4th 2021

    Created a Properties section and added a proposition stating the orthogonal factorisation system on Cof. Full proof will be filled in later. Added further examples of cofunctors. Added further references (papers by Garner) and some brief comments about each.

    I’m also wondering: there must be a link to the notion of comorphism, but it is not obvious to me. Does anyone have an idea? There are a variety of notions of comorphism in the Higgins-Mackenzie paper, so perhaps that provides is related.

    diff, v6, current

    • CommentRowNumber7.
    • CommentAuthorBryceClarke
    • CommentTimeAug 9th 2021
    • (edited Aug 9th 2021)

    Added link to Spivak-Niu draft textbook chapter on cofunctors, and the proposition that Cof\mathbf{Cof} is the category of comonoids in Poly(1,1)\mathbf{Poly}(1, 1).

    diff, v7, current

    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeMar 23rd 2023

    Mention “retrofunctor” terminology. From people I’ve spoken to, there is general consensus that this is a more appropriate, and less misleading, name than “cofunctor”. However, it probably isn’t appropriate to rename this page until there are more references using this terminology.

    diff, v8, current

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeNov 3rd 2023

    Rename page to “retrofunctor” rather than “cofunctor”, and added a note on terminology. Although this usage is still nascent in the literature, it is increasing in popularity (see for instance recent talk slides by Bryce Clarke [1] [2]), and avoids the misleading connotations of the “co-” prefix in “cofunctor”. Furthermore, it matches the terminology of monad retromorphism.

    diff, v10, current

    • CommentRowNumber10.
    • CommentAuthorvarkor
    • CommentTimeAug 16th 2024

    Mention cocategories in relation to the “cofunctor” terminology.

    diff, v13, current

  11. I hope it’s ok to remove a few instances of ” where a′=cod(φ 1(a,u))a' = cod(\varphi_{1}(a, u))”. I’ve read this page many times and always get confused by it. It seems like saying “f:X→Yf:X\to Y where Y=cod(f)Y = cod(f)” - it doesn’t add any new information and just trips me up wondering why it’s mentioned.

    Nathaniel Virgo

    diff, v15, current

1 to 11 of 11

  1.