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: Yoneda embedding

Bottom of Page

1 to 21 of 21

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2010

    Added Eric’s illustrations to the Idea-section at Yoneda embedding.

    • CommentRowNumber2.
    • CommentAuthorPeter Heinig
    • CommentTimeJun 19th 2017
    • (edited Jun 19th 2017)

    Yoneda embedding had

    If the Yoneda embedding of a category has a left adjoint, then that category is called a total category

    in the section “Properties” which appeared wrong on two accounts:

    • this is hardly a “property” of the Yoneda embedding
    • the same information was (and still is) given immediately below, under “Related concepts”, which seems the right place.

    Simply deleted the cited sentence.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJun 19th 2017

    I’ve reverted this. I don’t know what you mean by “this is hardly a property”, and I think it makes sense to include there.

  4. It’s a definition of the words “total category”, rather than a property. It does seem weird for it to appear twice in a row.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJun 19th 2017

    I view the “Related concepts” as a sort of index or summary of the other concepts that are related to this one. The fact that something is mentioned there doesn’t mean it shouldn’t appear somewhere else on the page; rather the opposite, if something is related then it should be mentioned somewhere in the main text of the page.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 19th 2017

    Yes, the section “Related concepts” is to play the role of a link list that contains everything that a reader of that entry might also want to check out. Ideally all of these keywords would also be explained a bit in the main text.

    In a case like this where the main text also does not do much more than just mention a keyword, the best solution would be to expand that line into a more comprehensive paragraph.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 19th 2017

    When the Yoneda embedding of a category has the property of having a left adjoint, we call that category total. It’s not a property true of all Yoneda embeddings obviously, but it is a notable property. :-)

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 19th 2017

    (It may be true that many if not most “Properties” sections of nLab articles are lists of properties that are necessary consequences of the concept under discussion. If that were a universal rule, then Peter had a point. I doubt this ever came up for discussion though, and I’m not sure it’s a good idea to box ourselves in with lists of rules about formatting. One rule of thumb though has been to trust each other to write sensibly, and above all to ask first before erasing someone’s work unless it’s obviously wrong – this last I feel is very important.)

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeDec 30th 2018
    • (edited Dec 30th 2018)

    I edited this page (Yoneda embedding) to add a link to restricted Yoneda embedding, but the link is not showing up on the page even when I shift+reload it, although if I edit it again the link is still there in the source.

  10. Thanks for letting me know. I’ll look into it later, please leave the source as it is currently (i.e. including the link that is not displaying) until then.

  11. Hi Mike, I just made a trivial edit, and it went through now. I don’t know what happened there, there are no errors in the logs. Just let me know if it happens again.

    • CommentRowNumber12.
    • CommentAuthorMike Shulman
    • CommentTimeDec 30th 2018

    Ok, thanks for looking at it.

    • CommentRowNumber13.
    • CommentAuthorMike Shulman
    • CommentTimeApr 10th 2019

    Added remark about existence of the notation よ.

    diff, v32, current

    • CommentRowNumber14.
    • CommentAuthorKeith Harbaugh
    • CommentTimeApr 11th 2019
    "The Yoneda embedding is sometimes denoted by よ, the hiragana kata for “Yo”."
    Could you give a reference for that? Thanks.
    • CommentRowNumber15.
    • CommentAuthorMike Shulman
    • CommentTimeApr 11th 2019

    Here.

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2019

    So that pointer to references deserves to be added to the entry.

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2019

    added the pointers to the notation references here that Ingo had provided (here)

    diff, v33, current

    • CommentRowNumber18.
    • CommentAuthorMike Shulman
    • CommentTimeApr 12th 2019

    Wouldn’t it be better to just include the first such usage (which is probably the Johnson-Freyd–Scheimbauer paper)?

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2019

    To be frank, I don’t understand this question. But it’s not important to me either way.

  20. Remove unnecessary duplication of “kana” from *”hiragana kana” c.f. *”PIN (personal identification number) number”, *”ATM (automatic teller machine) machine”.

    diff, v40, current

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeMay 10th 2024

    made explicit (here) the argument that the Yoneda embedding preserves limits

    diff, v41, current

1 to 21 of 21

  1.