5 citations · 8 across the 18 of their papers we have counts for
20 papers
An algebraic model for rational ultracommutative rings
William Balderrama, Jack Morgan Davies, Sil Linskens
Given a global equivariant ultracommutative ring spectrum and inclusion of finite groups, one may apply geometric fixed points to the norm $N_H^G E_H \to E…
Free algebras via monoidal envelopes
Max Blans, Sil Linskens
For any morphism of -operads , we show that the free -algebra on a -algebra admits an explicit formula as the colimit…
Ambidextrous global spectra and tempered cohomology
William Balderrama, Jack Morgan Davies, Sil Linskens
We introduce generalizations of global equivariant spectra which encode globally equivariant cohomology theories equipped with additional transfers, such as the deflation maps pres…
Affineness and reconstruction in complex-periodic geometry
William Balderrama, Jack Morgan Davies, Sil Linskens
Working in a generic derived algebro-geometric context, we lay the foundations for the general study of affineness and local descendability. When applied to rin…
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)_…
On the derived Tate curve and global smooth Tate -theory
Jack Morgan Davies, Sil Linskens
The interplay between equivariant stable homotopy theory and spectral algebraic geometry is used to construct a derived Tate curve over , a lift of the classical…
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…
Parametrised functor calculus: excision, spheres, and semiadditivity
Kaif Hilman, Sil Linskens
We lay down the foundations of a theory of parametrised functor calculus, generalising parts of the functor calculus of Goodwillie. We introduce the notion of excisable posets and…
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…
Global spaces and the homotopy theory of stacks
Adrian Clough, Bastiaan Cnossen, Sil Linskens
We show that the -category of global spaces is equivalent to the homotopy localization of the -category of sheaves on the site of separated differentiable stacks, f…
Global 2-rings and genuine refinements
David Gepner, Sil Linskens, Luca Pol
We introduce the notion of a naive global 2-ring: a functor from the opposite of the -category of global spaces to presentably symmetric monoidal stable -categories…
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…
Globalizing and stabilizing global -categories
Sil Linskens
We consider the question of cocompleting partially presentable parametrized -categories in the sense of arXiv:2307.11001. As our main result we show that in certain cases o…
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…
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…
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…
Global homotopy theory via partially lax limits
Sil Linskens, Denis Nardin, Luca Pol
We provide new -categorical models for unstable and stable global homotopy theory. We use the notion of partially lax limits to formalize the idea that a global object is a…
Two-variable fibrations, factorisation systems and -categories of spans
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We prove a universal property for -categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the s…
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We provide a calculus of mates for functors to the -category of -categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformat…