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arxiv: 0905.0462 · v2 · submitted 2009-05-04 · 🧮 math.CT · math.AT

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(Infinity,2)-Categories and the Goodwillie Calculus I

Jacob Lurie
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classification 🧮 math.CT math.AT
keywords categoriesinfinitycalculusgoodwillietheoryapplicationsbulkcase
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The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also considered). Our ultimate goal is to lay the foundations for a study of Tom Goodwillie's calculus of functors. To this end, we have included some simple applications to the theory of first derivatives.

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