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Mackey 2-Functors and Mackey 2-Motives

Balmer, Paul,

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Mackey 2-Functors and Mackey 2-Motives

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mackey 2-Functors and Mackey 2-Motives/ Paul Balmer, Ivo Dell'Ambrogio
作者:	Balmer, Paul,
其他作者:	Dell'Ambrogio, Ivo,
出版者:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2020,
面頁冊數:	1 online resource (235 pages)
標題:	Mathematics and science -
電子資源:	https://doi.org/10.4171/209
電子資源:	https://www.ems-ph.org/img/books/balmer_mini.jpg
ISBN:	9783037197097

Mackey 2-Functors and Mackey 2-Motives
Balmer, Paul,

Mackey 2-Functors and Mackey 2-Motives[electronic resource] /Paul Balmer, Ivo Dell'Ambrogio - Zuerich, Switzerland :European Mathematical Society Publishing House,2020 - 1 online resource (235 pages) - EMS Monographs in Mathematics (EMM) ;2523-5192.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

This book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2-functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists. The book contains an extended catalogue of examples of such Mackey 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples and the separable monadicity theorem explains how the value of a Mackey 2-functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology. The second part of the book provides a motivic approach to Mackey 2-functors, 2-categorifying the well-known span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshida's crossed Burnside ring are the universal source of block decompositions. The book is self-contained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interested in category theory, representation theory and topology.

ISBN: 9783037197097

Standard No.: 10.4171/209doiSubjects--Topical Terms:

3481059
Mathematics and science

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