23 citations · 33 across the 11 of their papers we have counts for
8 papers · 1 filter
On periodic homotopy and homology equivalences of spaces
Shaul Barkan, Gijs Heuts, Yuqing Shi
There are at least two ways to approach the homotopy theory of spaces `at chromatic height ': one may localize with respect to -homology or with respect to -periodic…
Open 2D TFTs admit initial open-closed extensions
Shaul Barkan, Jan Steinebrunner, Adela YiYu Zhang
We show that any open 2-dimensional topological field theory valued in a symmetric monoidal -category (with suitable colimits) extends canonically to an open-closed field t…
Cellularity of Chromatic Synthetic Spectra
Shaul Barkan, Sven van Nigtevecht
We show that the -category of synthetic spectra based on Morava E-theory is generated by the bigraded spheres and identify it with the -category of modules over a f…
Chromatic Homotopy is Monoidally Algebraic at Large Primes
Shaul Barkan
Fix a prime and a chromatic height . We prove that the homotopy -category of -local spectra is algebraic as a symmetric…
Segalification and the Boardman-Vogt tensor product
Shaul Barkan, Jan Steinebrunner
We develop an analog of Dugger and Spivak's necklace formula providing an explicit description of the Segal space generated by an arbitrary simplicial space. We apply this to obtai…
Explicit Square Zero Obstruction Theory
Shaul Barkan
We develop square zero obstruction theory for modules over -algebras in an arbitrary stable (presentably) monoidal -category. We explicitly describe the obstr…
The equifibered approach to -properads
Shaul Barkan, Jan Steinebrunner
We define a notion of -properads that generalises -operads by allowing operations with multiple outputs. Specializing to the case where each operation has a single…
Arity Approximation of -Operads
Shaul Barkan
Let denote the little discs operad for and let be an -category all of whose mapping spaces are -truncated. We prove tha…