28 citations · 127 across the 15 of their papers we have counts for
16 papers
Parametrized and equivariant higher algebra
Denis Nardin, Jay Shah
We develop the rudiments of a theory of parametrized -operads, including parametrized generalizations of monoidal envelopes, Day convolution, operadic left Kan extensions,…
On the equivalence of two theories of real cyclotomic spectra
J. D. Quigley, Jay Shah
We give a new formula for real topological cyclic homology that refines the fiber sequence formula discovered by Nikolaus and Scholze for topological cyclic homology to one involvi…
On the parametrized Tate construction
J. D. Quigley, Jay Shah
We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension of a finite group by a compact Lie group , which we…
Recollements and stratification
Jay Shah
We develop various aspects of the theory of recollements of -categories, including a symmetric monoidal refinement of the theory. Our main result establishes a formula for…
Parametrized higher category theory II: Universal constructions
Jay Shah
We develop parametrized generalizations of a number of fundamental concepts in the theory of -categories, including factorization systems, free fibrations, exponentiable fi…
Dualizable objects in stratified categories and the 1-dimensional bordism hypothesis for recollements
Grigory Kondyrev, Aaron Mazel-Gee, Jay Shah
Given a monoidal -category equipped with a monoidal recollement, we give a simple criterion for an object in to be dualizable in terms of the dualizability of each…
Scheiderer motives and equivariant higher topos theory
Elden Elmanto, Jay Shah
We give an algebro-geometric interpretation of -equivariant stable homotopy theory by means of the -topology introduced by Claus Scheiderer in his study of -torsion phen…
On the parametrized Tate construction and two theories of real -cyclotomic spectra
J. D. Quigley, Jay Shah
We give a new formula for -typical real topological cyclic homology that refines the fiber sequence formula discovered by Nikolaus and Scholze for -typical topological cyclic…
C_2-equivariant stable homotopy from real motivic stable homotopy
Mark Behrens, Jay Shah
We give a method for computing the C_2-equivariant homotopy groups of the Betti realization of a p-complete cellular motivic spectrum over R in terms of its motivic homotopy groups…
Parametrized higher category theory
Jay Shah
We develop foundations for the category theory of -categories parametrized by a base -category. Our main contribution is a theory of indexed homotopy limits and col…
Algorithmic canonical stratifications of simplicial complexes
Ryo Asai, Jay Shah
We introduce a new algorithm for the structural analysis of finite abstract simplicial complexes based on local homology. Through an iterative and top-down procedure, our algorithm…
Categorifying rationalization
Clark Barwick, Saul Glasman, Marc Hoyois +2
We solve a problem proposed by Khovanov by constructing, for any set of primes , a triangulated category (in fact a stable -category) whose Grothendieck group is $S^{-1}…
Parametrized higher category theory and higher algebra: Exposé I -- Elements of parametrized higher category theory
Clark Barwick, Emanuele Dotto, Saul Glasman +2
We introduce the basic elements of the theory of parametrized -categories and functors between them. These notions are defined as suitable fibrations of -categories…
Parametrized higher category theory and higher algebra: A general introduction
Clark Barwick, Emanuele Dotto, Saul Glasman +2
We introduce the study of parametrized higher category theory and parametrized higher algebra, and we describe the main theorems of the series of Exposés that make up the monograph…
Fibrations in -category theory
Clark Barwick, Jay Shah
In this short expository note, we discuss, with plenty of examples, the bestiary of fibrations in quasicategory theory. We underscore the simplicity and clarity of the construction…
Spectral Mackey functors and equivariant algebraic K-theory (II)
C. Barwick, S. Glasman, J. Shah
We study the "higher algebra" of spectral Mackey functors, which the first named author introduced in Part I of this paper. In particular, armed with our new theory of symmetric pr…