2 citations · 4 across the 12 of their papers we have counts for
13 papers
Hammock localization via Segal animae
Kensuke Arakawa, Bastiaan Cnossen
We give a short, conceptual account of Dwyer--Kan's hammock localization in the setting of -categories. Starting from Mazel-Gee's formula for localization via the relative…
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)_…
A short proof of the universality of the relative Rezk nerve
Kensuke Arakawa, Bastiaan Cnossen
We give a concise, conceptual proof of the universality of the relative Rezk nerve, due to Mazel-Gee.
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…
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…
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…
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…
Twisted ambidexterity in equivariant homotopy theory
Bastiaan Cnossen
We develop the concept of twisted ambidexterity in a parametrized presentably symmetric monoidal -category, which generalizes the notion of ambidexterity by Hopkins and Lur…
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…
Characters and transfer maps via categorified traces
Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi +1
We develop a theory of generalized characters of local systems in -categories, which extends classical character theory for group representations and, in particular, the in…