02889nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001400168084003600182100002700218245010000245260008200345300003400427336002600461337002600487338003600513347002400549490005300573506006600626520150800692650003602200650004202236650004602278650002002324650002802344700003302372856003202405856006602437256-200706CH-001817-320200706233004.0a fot ||| 0|cr nn mmmmamaa200706e20200804sz fot ||| 0|eng d a978303719709770a10.4171/2092doi ach0018173 7aP2bicssc a20-xxa18-xxa19-xxa55-xx2msc1 aBalmer, Paul,eauthor.10aMackey 2-Functors and Mackey 2-Motivesh[electronic resource] /cPaul Balmer, Ivo Dell'Ambrogio3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (235 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis 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.07aMathematics and science2bicssc07aGroup theory and generalizations2msc07aCategory theory; homological algebra2msc07a$K$-theory2msc07aAlgebraic topology2msc1 aDell'Ambrogio, Ivo,eauthor.40uhttps://doi.org/10.4171/209423cover imageuhttps://www.ems-ph.org/img/books/balmer_mini.jpg