Goodwillie Approximations to Higher Categories.

Cover
Title page
Introduction
Chapter 1. Main results
Chapter 2. Constructing -excisive approximations
Chapter 3. Another construction of polynomial approximations
Chapter 4. Coalgebras in stable ∞-operads
4.1. Truncations of ∞-operads
4.2. Coalgebras in a corepresentable ∞-operad
4.3. Coalgebras in an -truncated stable ∞-operad
Chapter 5. The space of Goodwillie towers
5.1. The Tate diagonal
5.2. Constructing -stages
5.3. A classification of -stages
5.4. The case of vanishing Tate constructions
Chapter 6. Examples
6.1. Divided power coalgebras and Koszul duality
6.2. Rational homotopy theory
6.3. Spaces with homotopy groups in a finite range
6.4. Spaces and Tate coalgebras
6.5. Further remarks on the Goodwillie tower of the homotopy theory of spaces
Appendix A. Compactly generated ∞-categories
Appendix B. Some facts from Goodwillie calculus
Appendix C. Truncations
C.1. The homotopy theory of truncated ∞-operads
C.2. Truncations of stable ∞-operads
C.3. A cobar construction for stable ∞-operads
C.4. Coalgebras
Bibliography
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