8 papers · 1 filter
Norms in equivariant homotopy theory
Tobias Lenz, Sil Linskens, Phil Pützstück
We show that the -category of normed algebras in genuine -spectra, as introduced by Bachmann-Hoyois, is modelled by strictly commutative algebras in -symmetric spectr…
Parametrized stability and the universal property of global spectra
Bastiaan Cnossen, Tobias Lenz, Sil Linskens
We develop a framework of parametrized semiadditivity and stability with respect to so-called atomic orbital subcategories of an indexing -category , extending work of N…
Mackey functors and classical equivariant -theory
Tobias Lenz
We show that the spectral Mackey functors associated to the equivariant algebraic -theory spectra of Guillou-May and Merling (originally constructed using pointset models) can b…
Global homotopy theory via spectral Mackey functors
Tobias Lenz
We show that Hausmann's model of global stable homotopy theory in terms of symmetric spectra is equivalent to the -category of spectral Mackey functors in the sense of Barw…
Parametrized (higher) semiadditivity and the universality of spans
Bastiaan Cnossen, Tobias Lenz, Sil Linskens
Semiadditivity of an -category, i.e. the existence of biproducts, provides it with useful algebraic structure in the form of a canonical enrichment in commutative monoids.…
Partial parametrized presentability and the universal property of equivariant spectra
Bastiaan Cnossen, Tobias Lenz, Sil Linskens
We introduce a notion of partial presentability in parametrized higher category theory and investigate its interaction with the concepts of parametrized semiadditivity and stabilit…