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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 $P_n \colon [\mathcal{C}, \mathcal{D}] \to Exc^n(\mathcal{C}, \mathcal{D})$ 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.

• 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.