English
A survey of Mackey and Green 2-functors
Multi angle
Auteurs : Dell'Ambrogio, Ivo (Auteur de la Conférence)
CIRM (Editeur )
18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories), See also {20Axx, 20Lxx, 20Mxx}
20J05 - Homological methods in group theory
55P91 - Equivariant homotopy theory, See also {19L47}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2339/Slides/DellAmbrogio-ChroK.pdf
CIRM (Editeur )
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Résumé :
Since the early 70s, Mackey and Green functors have been successfully used to model the induction and restriction maps which are ubiquitous in the representation theory of finite groups. In concrete examples, the latter maps are typically distilled, in some way, from induction and restriction functors between additive (abelian, triangulated...) categories. In order to better capture this richer layer of equivariant information with a (light!) set of axioms, we are naturally led to the notions of Mackey and Green 2-functors. Many such structures have been in use for a long time in algebra, geometry and topology. We survey examples and applications of this young—yet arguably overdue—theory. This is partially joint work with Paul Balmer and Jun Maillard.
Keywords : Mackey functors; Green functors; finite groups; 2-categories
Codes MSC : Keywords : Mackey functors; Green functors; finite groups; 2-categories
18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories), See also {20Axx, 20Lxx, 20Mxx}
20J05 - Homological methods in group theory
55P91 - Equivariant homotopy theory, See also {19L47}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2339/Slides/DellAmbrogio-ChroK.pdf
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 17/02/2023 Date de captation : 23/01/2023 Sous collection : Research talks arXiv category : Algebraic Topology ; Atmospheric and Oceanic Physics Domaine : Algebra ; Topology Format : MP4 (.mp4) - HD Durée : 00:57:26 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-01-23_Dell'Ambrogio.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteursOrganisateurs de la rencontre : Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine Dates : 23/01/2023 - 27/01/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2339.html
Données de citation
DOI : 10.24350/CIRM.V.19996703Citer cette vidéo: Dell'Ambrogio, Ivo (2023). A survey of Mackey and Green 2-functors. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19996703 URI : http://dx.doi.org/10.24350/CIRM.V.19996703 |
Voir aussi
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Auteur de la Conférence Zakharevich, Inna.
- [Multi angle] On the stable cohomology of the automorphism groups of free groups with coefficients / Auteur de la Conférence Vespa, Christine.
- [Multi angle] Representation spheres and chromatic Picard groups / Auteur de la Conférence Stojanoska, Vesna.
- [Multi angle] How algebraic is a stable model category? / Auteur de la Conférence Roitzheim, Constanze.
- [Multi angle] Topological cyclic homology of the second truncated Brown–Peterson spectrum / Auteur de la Conférence Rognes, John.
- [Multi angle] Equivalences in higher categories / Auteur de la Conférence Ozornova, Viktoriya.
- [Multi angle] (2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem / Auteur de la Conférence Osorno, Angélica.
- [Multi angle] Equivariant homotopy theory for infinite groups and THH with coefficients / Auteur de la Conférence Nikolaus, Thomas.
- [Multi angle] Equivariant elliptic cohomology / Auteur de la Conférence Meier, Lennart.
- [Multi angle] The universal property of topological Hochschild homology / Auteur de la Conférence Harpaz, Yonatan.
- [Multi angle] Prismatic and syntomic cohomology of ring spectra / Auteur de la Conférence Hahn, Jeremy.
- [Multi angle] Spaces of quasi-invariants / Auteur de la Conférence Berest, Yuri.
- [Multi angle] The chromatic Nullstellensatz / Auteur de la Conférence Burklund, Robert.
- [Multi angle] Adjoining roots to ring spectra and algebraic K-theory / Auteur de la Conférence Bayindir, Haldun Özgür.
Bibliographie
- BALMER, Paul et DELL'AMBROGIO, Ivo. Mackey 2-Functors and Mackey 2-Motives. 2020. - https://doi.org/10.4171/209
- BALMER, Paul et DELL'AMBROGIO, Ivo. Green equivalences in equivariant mathematics. Mathematische Annalen, 2021, vol. 379, no 3-4, p. 1315-1342. - http://dx.doi.org/10.1007/s00208-021-02145-2
- DELL'AMBROGIO, Ivo. Green 2-functors. Transactions of the American Mathematical Society, 2022, vol. 375, no 11, p. 7783-7829. - http://dx.doi.org/10.1090/tran/8681
- MAILLARD, Jun. A categorification of the Cartan-Eilenberg formula. Advances in Mathematics, 2022, vol. 396, p. 108187. - https://doi.org/10.1016/j.aim.2022.108187
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