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Showing 1 to 6 of 6 for “"Taylor Tower"”.
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Computing the Goodwillie-Taylor tower of discrete modules
… the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. …
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Computing the Goodwillie-Taylor tower for discrete modules
A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from …
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Obstructions to Constructing the Taylor Tower of Finite Degree Functors of Spectra
… thesis, we introduce a new way to construct the Taylor tower of a (homotopy, reduced and finite degree) functor F from spectra to spectra. As a result, the notion of Tate obstructions as defined by Randy McCarthy is studied and generalized to the notion of higher order obstructions. These …
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Cosimplicial invariants and Calculus of homotopy functors
… by Waldhausen (using a variant of Goodwillie’s Taylor tower). The proof of agreement of these constructions relies heavily on the fact that the functors involved take values in Spectra. Goodwillie conjectured the extension of these results to include the case of functors taking value in Spaces. …
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Beyond orthogonal calculus: the unitary and real cases
… the complex vector spaces. These calculi produce Taylor towers approximating a functor, and we show through a zig-zag of Quillen equivalences (in both versions of the calculi) that the layers of these towers are classified by spectra with an action of either U(n) in the unitary case, or the …
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Goodwillie calculus and algebras over a spectral operad
… between such categories; identifying the Taylor tower of the identity in those categories; showing that finitary n-excisive functors can not distinguish between Algo and Algo,, the category of algebras over the truncated operad O<; and a weak form of the chain rule between the algebra …