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: Yoneda lemma

Bottom of Page

101 to 107 of 107

  1. <
  2. 1
  3. 2
  4. >

  1. Section “Necessity of naturality” sounded like there is nothing interesting going on if we look at the unnatural isomorphism of hom-sets. But this isn’t the case, already in the 60s a graph-theoretical and purely categorical facts of this form have been established. I’m adding the two earliest references.

    Tomas Jakl

    diff, v72, current

    • CommentRowNumber102.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2021
    • (edited Jun 18th 2021)

    The entry fell short of really citing the following in full, so I have added it now:

    diff, v73, current

  3. adding text from HoTT wiki.

    Anonymous

    diff, v76, current

    • CommentRowNumber104.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    This edit needs analogous adjustments to those pointed out in another thread here.

    I am out of energy for the moment. Please look into it. Generally, please try to keep in mind that nLab entries need to retain a minimum of logical consistency as you drop material into them that is copied from elsewhere.

    diff, v77, current

    • CommentRowNumber105.
    • CommentAuthorkrinsman
    • CommentTimeMar 31st 2024
    Would it be OK to edit the page to use consistent notation for Hom sets throughout? (Or at least for the Hom sets of the generic category "C"?)

    At one point in the article they're denoted Hom_C (...), but elsewhere they're denoted C(...).

    Of course changing it from the latter would require then changing the notation for the Hom-sets of other categories mentioned, e.g. Set(...) to Hom_Set (...).

    I'm willing to scan through the article and make the change to either convention, it's just unclear to me which convention should be preferred.

    Having two distinct conventions (or no notice / warning of the switch between them) seems like it would be very confusing to someone using this article as an introduction. (And is honestly somewhat jarring to me even as someone already moderately familiar with the topic.)
    • CommentRowNumber106.
    • CommentAuthorUrs
    • CommentTimeMar 31st 2024

    This happens when different authors edit different bits at different times.

    If you have the energy to harmonize the notation, it would be a welcome service to the community.

    The notation C(...)C(...) tends to indicate that the construction also works in the enriched context, while the notation Hom C(...)Hom_C(...) makes clear that one does insist to mean plain Hom-sets.

    So I suppose that C(...)C(...) is a good choice for this page.

  7. Rename parameter of the inverse of the Yoneda map to clarify that the “functional” component of (X(c)\to (C(-,c)\to X(d)) comes from the (C(-,c)) component, not the (X(c)) component.

    This also keeps notation more consistent with the forward direction.

    Dov Mostovicz

    diff, v82, current

101 to 107 of 107

  1. <
  2. 1
  3. 2
  4. >