Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Goodwillie approximations to higher categories   We construct a Goodwillie tower of categories which interpolates between the
category of pointed spaces and the category of spectra. This tower of
categories refines the Goodwillie tower of the identity functor in a precise
sense. More generally, we construct such a tower for a large class of
infinity-categories C. We classify such Goodwillie towers in terms of the
derivatives of the identity functor of C. As a particular application we show
how this provides a model for the homotopy theory of simply-connected spaces in
terms of coalgebras with Tate diagonals. Our classification of Goodwillie
towers simplifies considerably in settings where the Tate cohomology of the
symmetric groups vanishes. As an example we apply our methods to rational
homotopy theory. Another application identifies the homotopy theory of p-local
spaces with homotopy groups in a certain finite range with the homotopy theory
of certain algebras over Ching's spectral version of the Lie operad. This is a
close analogue of Quillen's results on rational homotopy. In the sequel to this
paper we work out consequences for the study of $v_n$-periodic unstable
homotopy theory and the Bousfield-Kuhn functors.

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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th