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Mackey Profunctors
About this Title
D. Kaledin
Publication: Memoirs of the American Mathematical Society
Publication Year:
2022; Volume 280, Number 1385
ISBNs: 978-1-4704-5536-1 (print); 978-1-4704-7285-6 (online)
DOI: https://doi.org/10.1090/memo/1385
Published electronically: October 7, 2022
Table of Contents
Chapters
- Acknowledgments
- Introduction
- 1. Preliminaries
- 2. Recollection on Mackey functors
- 3. Mackey profunctors
- 4. Generalities on the $S$-construction
- 5. Additivization
- 6. Derived Mackey profunctors
- 7. Mackey functors and representations
- 8. Derived normal systems
- 9. The cyclic group case
Abstract
In the standard theory of Mackey functors for a group $G$, the group is either finite, or a compact Lie group. In the present paper, we develop an alternative notion of a Mackey profunctor that works better for profinite groups. The most important practical example is $G=\widehat {\mathbb {Z}}$, the profinite completion of the group of the integers, and in this case, our Mackey profunctors appear naturally in the theory of cyclotomic traces.- Clark Barwick, Spectral Mackey functors and equivariant algebraic $K$-theory (I), Adv. Math. 304 (2017), 646–727. MR 3558219, DOI 10.1016/j.aim.2016.08.043
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