Homotopy Theory of Enriched Mackey Functors: Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors

This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structures provide deeper and more robust applications. With an eye to such applications, this work provides further development of both the categorical algebra of enriched diagrams, and the homotopy theoretic applications in K-theory spectra. The title refers to certain enriched presheaves, known as Mackey functors, whose homotopy theory classifies that of equivariant spectra. More generally, certain stable model categories are classified as modules - in the form of enriched presheaves - over categories of generating objects. This text contains complete definitions, detailed proofs, and all the background material needed to understand the topic. It will be indispensable for graduate students and researchers alike.

Author: Niles Johnson, Donald Yau
Binding Type: Paperback
Publisher: Cambridge University Press
Published: 02/06/2025
Series: London Mathematical Society Lecture Note #492
Pages: 523
Weight: 1.62lbs
Size: 8.90h x 6.17w x 1.07d
ISBN: 9781009519526