6 citations · 16 across the 19 of their papers we have counts for
21 papers
Global -categories and global Thom spectra
Emma Brink, Tobias Lenz
We introduce a framework of (Lie-)global -categories, which formalizes various families of -categories indexed by compact Lie groups and equipped with suitable rest…
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…
Revisiting -naturality of the Yoneda embedding
Tobias Lenz
We show that the Yoneda embedding 'is' -natural with respect to the functoriality of presheaves via left Kan extension, refining the -categorical result pro…
Universality of span 2-categories and the construction of 6-functor formalisms
Bastiaan Cnossen, Tobias Lenz, Sil Linskens
Given an -category equipped with suitable wide subcategories , we show that the -category $\text{S}{\scriptstyle\text{PAN}}_2(C,E)_…
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…
Universality of Barwick's unfurling construction
Bastiaan Cnossen, Tobias Lenz, Maxime Ramzi
Given an -category with pullbacks, its -category of spans has the universal property of freely adding right adjoints…
Normed equivariant ring spectra and higher Tambara functors
Bastiaan Cnossen, Rune Haugseng, Tobias Lenz +1
In this paper we extend equivariant infinite loop space theory to take into account multiplicative norms: For every finite group , we construct a multiplicative refinement of th…
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.…
Homotopical commutative rings and bispans
Bastiaan Cnossen, Rune Haugseng, Tobias Lenz +1
We prove that commutative semirings in a cartesian closed presentable -category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors fr…
The Adams isomorphism revisited
Bastiaan Cnossen, Tobias Lenz, Sil Linskens
We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable equivariantly semiadditive global category. This encompasses the well-known Adams isomorphism in…
Simplicial -modules and mild actions
Tobias Lenz, Anna Marie Schröter
We develop an analogue of the theory of -modules in the world of simplicial sets, based on actions of a certain simplicial monoid originally appearing in the const…
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…
Global model categories and topological André-Quillen cohomology
Tobias Lenz, Michael Stahlhauer
We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, g…
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…
Genuine vs. naïve symmetric monoidal G-categories
Tobias Lenz
We prove that through the eyes of equivariant weak equivalences the genuine symmetric monoidal -categories of Guillou and May [Algebr. Geom. Topol. 17 (2017), no. 6, 3259-3339;…
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…
Categorical models of unstable G-global homotopy theory
Tobias Lenz
We prove that the category of small categories with -action forms a model of unstable -global homotopy theory for every discrete group , generalizing Schw…
G-Global Homotopy Theory and Algebraic K-Theory
Tobias Lenz
We develop the foundations of -global homotopy theory as a synthesis of classical equivariant homotopy theory on the one hand and global homotopy theory in the sense of Schwede…
On the global homotopy theory of symmetric monoidal categories
Tobias Lenz
Parsummable categories were introduced by Schwede as input for his global algebraic -theory construction. We prove that their whole homotopy theory with respect to the so-called…
Parsummable categories as a strictification of symmetric monoidal categories
Tobias Lenz
We prove that the homotopy theory of parsummable categories (as defined by Schwede) with respect to the underlying equivalences of categories is equivalent to the usual homotopy th…
Homotopy (Pre-)Derivators of Cofibration Categories and Quasi-Categories
Tobias Lenz
We prove that the homotopy prederivator of a cofibration category is equivalent to the homotopy prederivator of its associated quasi-category of frames, as introduced by Szumiło. W…