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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 4th 2016

    I have created an entry-for-inclusion Goodwillie calculus - contents, and have included it as a “floating table of contents” into the relevant entries.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 5th 2016

    We’re using Goodwillie calculus as a synonym for ’calculus of functors’?

    Wikipedia’s page claims there are three branches

    • manifold calculus, such as embeddings,
    • homotopy calculus, and
    • orthogonal calculus.

    The references at Goodwillie calculus are for the first and second, but there seems no mention of the third.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2016
    • (edited Jan 5th 2016)

    I am referring to the tower of reflections P n:[𝒞,𝒟]Exc n(𝒞,𝒟)P_n \colon [\mathcal{C}, \mathcal{D}] \to Exc^n(\mathcal{C}, \mathcal{D}) to nn-excisive functors (for suitable 𝒞\mathcal{C} and 𝒟\mathcal{D}). This is Goodwillie’s setup, some authors synonymously also call it “calculus of homotopy functors”, e.g. section 10.1 of

    “Cubical homotopy theory” (pdf)

    The “manifold calculus” is just a special case of this, see section 10.2 of this article.

    About “orthogonal calculus” I am not sure at the moment, would need to check.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 5th 2016

    There some comparison in Comparing the orthogonal and homotopy functor calculi by Barnes and Eldred.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2016

    all right, let’s start orthogonal calculus

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 5th 2016

    Added a paper by Michael Weiss.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2016

    Thanks. I have expanded the Idea-section accordingly, and cross-linked a bit more.

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