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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.01371 |
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| _version_ | 1866916323656728576 |
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| author | Dell'Ambrogio, Ivo |
| author_facet | Dell'Ambrogio, Ivo |
| contents | For half a century, 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 the examples, the latter maps are typically distilled in some way from induction and restriction functors between additive categories. This naturally leads to the notions of Mackey and Green 2-functors and to axioms which better capture this underlying layer of information. Such structures have been used in algebra, geometry and topology for a long time. We survey examples and applications of this young (yet arguably overdue) theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01371 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An introduction to Mackey and Green 2-functors Dell'Ambrogio, Ivo Representation Theory Group Theory K-Theory and Homology 20J05, 18B40, 18N10, 19A22 For half a century, 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 the examples, the latter maps are typically distilled in some way from induction and restriction functors between additive categories. This naturally leads to the notions of Mackey and Green 2-functors and to axioms which better capture this underlying layer of information. Such structures have been used in algebra, geometry and topology for a long time. We survey examples and applications of this young (yet arguably overdue) theory. |
| title | An introduction to Mackey and Green 2-functors |
| topic | Representation Theory Group Theory K-Theory and Homology 20J05, 18B40, 18N10, 19A22 |
| url | https://arxiv.org/abs/2305.01371 |