The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
1. Introduction
2. Detailed overview and fundamental examples
3. Stratified noncommutative geometry
4. Fundamental operations
5. The $\mathcal {O}$-monoidal reconstruction theorem
6. The geometric stratification of genuine $G$-spectra
7. The metacosm reconstruction theorem
8. Variations on the metacosm reconstruction theorem
A. Actions and limits, strict and lax
B. Some $(\infty ,2)$-category theory
David Ayala, Montana State University, Bozeman, Montana, Aaron Mazel-Gee, California Institute of Technology, Palo Alto, California, and Nick Rozenblyum, University of Chicago, Illinois.
