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作者 Balmer, Paul, author
書名 Mackey 2-Functors and Mackey 2-Motives [electronic resource] / Paul Balmer, Ivo Dell'Ambrogio
出版項 Zuerich, Switzerland : European Mathematical Society Publishing House, 2020
國際標準書號 9783037197097
國際標準號碼 10.4171/209 doi
book jacket
說明 1 online resource (235 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
系列 EMS Monographs in Mathematics (EMM) ; 2523-5192
附註 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
主題 Mathematics and science bicssc
Group theory and generalizations msc
Category theory; homological algebra msc
$K$-theory msc
Algebraic topology msc
Alt Author Dell'Ambrogio, Ivo, author
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