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A survey of Mackey and Green 2-functors
Multi angle
Authors : Dell'Ambrogio, Ivo (Author of the conference)
CIRM (Publisher )
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}
Additional resources :
https://www.cirm-math.fr/RepOrga/2339/Slides/DellAmbrogio-ChroK.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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}
Additional resources :
https://www.cirm-math.fr/RepOrga/2339/Slides/DellAmbrogio-ChroK.pdf
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 17/02/2023 Conference Date : 23/01/2023 Subseries : Research talks arXiv category : Algebraic Topology ; Atmospheric and Oceanic Physics Mathematical Area(s) : Algebra ; Topology Format : MP4 (.mp4) - HD Video Time : 00:57:26 Targeted 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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Information on the Event
Event Title : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteursEvent Organizers : Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine Dates : 23/01/2023 - 27/01/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2339.html
Citation Data
DOI : 10.24350/CIRM.V.19996703Cite this video as: 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 |
See Also
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Author of the conference Zakharevich, Inna.
- [Multi angle] On the stable cohomology of the automorphism groups of free groups with coefficients / Author of the conference Vespa, Christine.
- [Multi angle] Representation spheres and chromatic Picard groups / Author of the conference Stojanoska, Vesna.
- [Multi angle] How algebraic is a stable model category? / Author of the conference Roitzheim, Constanze.
- [Multi angle] Topological cyclic homology of the second truncated Brown–Peterson spectrum / Author of the conference Rognes, John.
- [Multi angle] Equivalences in higher categories / Author of the conference Ozornova, Viktoriya.
- [Multi angle] (2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem / Author of the conference Osorno, Angélica.
- [Multi angle] Equivariant homotopy theory for infinite groups and THH with coefficients / Author of the conference Nikolaus, Thomas.
- [Multi angle] Equivariant elliptic cohomology / Author of the conference Meier, Lennart.
- [Multi angle] The universal property of topological Hochschild homology / Author of the conference Harpaz, Yonatan.
- [Multi angle] Prismatic and syntomic cohomology of ring spectra / Author of the conference Hahn, Jeremy.
- [Multi angle] Spaces of quasi-invariants / Author of the conference Berest, Yuri.
- [Multi angle] The chromatic Nullstellensatz / Author of the conference Burklund, Robert.
- [Multi angle] Adjoining roots to ring spectra and algebraic K-theory / Author of the conference Bayindir, Haldun Özgür.
Bibliography
- 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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