Characters and transfer maps via categorified traces

Autor:	Carmeli, Shachar, Cnossen, Bastiaan, Ramzi, Maxime, Yanovski, Lior
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Topology Mathematics - Category Theory Mathematics - K-Theory and Homology
Druh dokumentu:	Working Paper
Popis:	We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is that we utilize the interaction between traces and their categorifications. We apply this theory to reprove and refine various results on the composability of Becker-Gottlieb transfers, the Hochschild homology of Thom spectra, and the additivity of traces in stable $\infty$-categories. Comment: 94 pages, comments welcome! v2: updated exposition and terminology in section 4.2
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.17364 Zobrazit plný text záznamu View this record from Arxiv