Title: Homotopy Theory of Enriched Mackey Functors: Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors: . Mathematical Society Lecture Note Series)
Publisher: Cambridge University Press CUP
Publication Date: 2025
Language: English
ISBN 10: 1009519522
ISBN 13: 9781009519526
Binding: Soft cover
Condition: New

About this title

Synopsis

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.

About the Authors

Niles Johnson is an Associate Professor of Mathematics at the Ohio State University at Newark. His research focuses on algebraic topology.

Donald Yau is a Professor of Mathematics at the Ohio State University at Newark. His research focuses on homotopy theory and algebraic K-theory.

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