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- W4300772406 abstract "For an equivariant commutative ring spectrum $R$, $pi_0 R$ has algebraic structure reflecting the presence of both additive transfers and multiplicative norms. The additive structure gives rise to a Mackey functor and the multiplicative structure yields the additional structure of a Tambara functor. If $R$ is an $N_infty$ ring spectrum in the category of genuine $G$-spectra, then all possible additive transfers are present and $pi_0 R$ has the structure of an incomplete Tambara functor. However, if $R$ is an $N_infty$ ring spectrum in a category of incomplete $G$-spectra, the situation is more subtle. In this paper, we study the algebraic theory of Tambara structures on incomplete Mackey functors, which we call bi-incomplete Tambara functors. Just as incomplete Tambara functors have compatibility conditions that control which systems of norms are possible, bi-incomplete Tambara functors have algebraic constraints arising from the possible interactions of transfers and norms. We give a complete description of the possible interactions between the additive and multiplicative structures." @default.
- W4300772406 created "2022-10-04" @default.
- W4300772406 creator A5044034295 @default.
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- W4300772406 date "2021-04-21" @default.
- W4300772406 modified "2023-09-27" @default.
- W4300772406 title "Bi-incomplete Tambara functors" @default.
- W4300772406 doi "https://doi.org/10.48550/arxiv.2104.10521" @default.
- W4300772406 hasPublicationYear "2021" @default.
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