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I have created an entry-for-inclusion Goodwillie calculus - contents, and have included it as a “floating table of contents” into the relevant entries.
We’re using Goodwillie calculus as a synonym for ’calculus of functors’?
Wikipedia’s page claims there are three branches
The references at Goodwillie calculus are for the first and second, but there seems no mention of the third.
I am referring to the tower of reflections $P_n \colon [\mathcal{C}, \mathcal{D}] \to Exc^n(\mathcal{C}, \mathcal{D})$ to $n$-excisive functors (for suitable $\mathcal{C}$ and $\mathcal{D}$). 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.
There some comparison in Comparing the orthogonal and homotopy functor calculi by Barnes and Eldred.
all right, let’s start orthogonal calculus
Added a paper by Michael Weiss.
Thanks. I have expanded the Idea-section accordingly, and cross-linked a bit more.
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