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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeDec 14th 2009

    Created extranatural transformation by moving the relevant information from dinatural transformation and adding the definition. Disagreements are welcome, but I feel that since dinaturals that aren't extranatural are so rare and harder to deal with and understand, extranaturals merit their own page.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeDec 14th 2009

    Looks good to me.

    • CommentRowNumber3.
    • CommentAuthorYaron
    • CommentTime5 days ago

    I have a (perhaps silly) question regarding the entry extranatural transformation. After Lemmas 1-3, it is stated that “In fact, these lemmas essentially capture “all possible” ways in which extranatural transformations can be composed. The general statement, which is obtained by combining these, is that if the graphs representing the two transformations can be composed without creating any closed loops, then the transformations can be composed, and the resulting graph is the composite of the individual graphs.”

    However, I don’t understand how, for example, the general version of yanking, where the domain of GG has any odd number of factors (Prop. 1 of Eilenberg-Kelly) follows by combining Lemmas 1-3 as stated. To really become the “general building blocks,” shouldn’t Lemma 1-3 be stated with any number of even (Lemma 1,2) or odd (Lemma 3) factors for the relevant transformations, as in Props. 1,2,2* of E-K?

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTime4 days ago

    That statement seems to be my fault. I’m not sure what I had in mind. Please fix it!

    • CommentRowNumber5.
    • CommentAuthorYaron
    • CommentTime4 days ago

    Sure. It will take me a day or two to get to it, and I will update when I’m done.

    • CommentRowNumber6.
    • CommentAuthorYaron
    • CommentTime4 days ago

    Done. I hope that all the right indices are there. I have also slightly changed the concluding sentence after Lemma 1-3.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTime4 days ago

    Thanks, Yaron!

    • CommentRowNumber8.
    • CommentAuthorYaron
    • CommentTime4 days ago

    Sure, my pleasure!

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTime3 days ago

    Nice, thanks!

    I wonder whether it would be worth stating the theorems in the simpler n=1n=1 case first, to help the reader’s intuition, before the general one with all the indices?

    • CommentRowNumber10.
    • CommentAuthorYaron
    • CommentTime3 days ago

    Sounds like a good idea.