36 citations · 193 across the 43 of their papers we have counts for
36 papers · 1 filter
Filtered spaces, filtered objects
Tyler Lawson
We introduce a operation on categories enriched in filtered spaces, whose effect is to turn categories of -pages into categories of -pages. This allows us to give a homot…
Synthetic spectra are (usually) cellular
Tyler Lawson
If is a connective ring spectrum, then Pstragowski's category of -synthetic spectra is generated by the bigraded spheres . In particular, it is equivalent t…
Examples of disk algebras
Sanath Devalapurkar, Jeremy Hahn, Tyler Lawson +2
We produce refinements of the known multiplicative structures on the Brown--Peterson spectrum , its truncated variants , Ravenel's spectra , and even…
On the slice spectral sequence for quotients of norms of Real bordism
Agnès Beaudry, Michael A. Hill, Tyler Lawson +2
In this paper, we investigate equivariant quotients of the Real bordism spectrum's multiplicative norm by permutation summands. These quotients are of interest b…
-pushouts and -tensors
Michael A. Hill, Tyler Lawson
We prove a general result that relates certain pushouts of -algebras to relative tensors over -algebras. Specializations include a number of established results on cl…
Skeleta and categories of algebras
Jonathan Beardsley, Tyler Lawson
We define a notion of a connectivity structure on an -category, analogous to a -structure but applicable in unstable contexts -- such as spaces, or algebras over an oper…
The homotopy types of free racks and quandles
Tyler Lawson, Markus Szymik
We initiate the homotopical study of racks and quandles, two algebraic structures that govern knot theory and related braided structures in algebra and geometry. We prove analogs o…
Quotient rings of
Agnes Beaudry, Michael A. Hill, Tyler Lawson +2
We study modules over the commutative ring spectrum , whose coefficient groups are quotients of the dual Steenrod algebra by collections of the Mil…
ring spectra and Dyer-Lashof operations
Tyler Lawson
This is an expository article about power operations and their connection with the study of highly structured ring spectra. In particular, we discuss Dyer-Lashof operations and the…
An introduction to Bousfield localization
Tyler Lawson
In this article we discuss Bousfield localization, beginning with definitions in terms of mapping spaces and working up to a discussion of how they can be constructed when we have…
Stable power operations
Saul Glasman, Tyler Lawson
For any ring spectrum , we show that there is an algebra of stable power operations that acts naturally on the underlying spectrum of any -algebr…
Unwinding the relative Tate diagonal
Tyler Lawson
We show that a spectral sequence developed by Lipshitz and Treumann, for application to Heegaard Floer theory, converges to a localized form of topological Hochschild homology with…
Adjoining roots in homotopy theory
Tyler Lawson
We use a "twisted group algebra" method to constructively adjoin formal radicals , for a unit in a commutative ring spectrum or an invertible object in a symmetric m…
The Witt vectors for Green functors
Andrew J. Blumberg, Teena Gerhardt, Michael A. Hill +1
We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology , and it describ…
Calculating obstruction groups for E-infinity ring spectra
Tyler Lawson
We describe a special instance of the Goerss-Hopkins obstruction theory, due to Senger, for calculating the moduli of ring spectra with given mod- homology. In partic…
Secondary power operations and the Brown-Peterson spectrum at the prime 2
Tyler Lawson
The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show t…
Brauer groups and Galois cohomology of commutative ring spectra
David Gepner, Tyler Lawson
In this paper we develop methods for classifying Baker-Richter-Szymik's Azumaya algebras over a commutative ring spectrum, especially in the largely inaccessible case where the rin…
Strictly commutative complex orientation theory
Michael J. Hopkins, Tyler Lawson
For a multiplicative cohomology theory E, complex orientations are in bijective correspondence with multiplicative natural transformations to E from complex bordism cohomology MU.…
Localization of enriched categories and cubical sets
Tyler Lawson
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched cat…
Topological modular forms with level structure
Michael Hill, Tyler Lawson
The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connecte…
A note on H_infinity structures
Tyler Lawson
We give a source of examples of H_infinity ring structures that do not lift to E_infinity ring structures, based on Mandell's equivalence between certain cochain algebras and space…
The Shimura curve of discriminant 15 and topological automorphic forms
Tyler Lawson
We find defining equations for the Shimura curve of discriminant 15 over Z[1/15]. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the hi…
A descent spectral sequence for arbitrary K(n)-local spectra with explicit -term
Daniel G. Davis, Tyler Lawson
Let n be any positive integer and p any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with…
Commutative ring objects in pro-categories and generalized Moore spectra
Daniel G. Davis, Tyler Lawson
We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along cert…