Talk:Yoneda lemma

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[edit] Commutative diagram

Is there any was of cleaning up the commutative diagram...unfortunately the AMS CD package doesn't work. One could convert to JPEG I suppose (YUCK)

PLEASE o please could we get rid of "Philosophy" as a title head? When somebody says "My philosophy of the matter is.." I usually expect complete garbage to follow. This is not an attack on Philosophy, quite the contrary, it's an attack on the continual devaluation of Philosophy as a subject of intellectual endeavor. To use it as synonym for vagueness is unfortunate. User:CSTAR

Well, philosophy is no more. It's quite an old article by WP standards, and probably needs work. More about representable functors, eg in homotopy theory, would be handy also.

Charles Matthews 20:17, 5 May 2004 (UTC)

I replaced the original ASCII diagram

    D --> Fun(Dop,Set)
    |          | 
    |          |
    |          |
    V          V
    C --> Fun(Cop,Set)

with the picture

Image:YonedaLemma-01.png

The original seemed backwards to me the way things were stated. Please let me know if I screwed it up (highly possible, as things like covariant functors into categories of contravariant functors really make my head hurt). -- Fropuff 16:55, 2004 Jul 20 (UTC)

[edit] Comment

Someone should probably say in what way the Yoneda lemma is a "vast generalisation of Cayley's theorem from group theory". Also, might be worth including the enriched-category version of the lemma as well. (hinted at at the bottom, but not stated explicitly) —The preceding unsigned comment was added by 134.226.81.3 (talk • contribs) 02:25, 20 January 2006.

Indeed. Feel free to make the edits yourself if you are so inclined. We always need more contributors -- Fropuff 05:02, 20 January 2006 (UTC)
It amounts to the same, but one can rephrase it as As a special case, when the category has only one object, and its morphisms correspond to the elements of a group, one recovers Cayley's theorem on realising a group as a permutation group.Hillgentleman 12:15, 11 September 2006 (UTC)
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