The Eilenberg-Watts theorem in homotopical algebra (2009)
The object of this paper is to prove that the standard categories in which homotopy theory is done, such as topological spaces, simplicial sets, chain complexes of abelian groups, and any of the...
Additive closed symmetric monoidal structures on R-modules (2009)
In this paper, we classify additive closed symmetric monoidal structures on the category of left R-modules by using Watts' theorem. An additive closed symmetric monoidal structure is equivalent to an...
The ghost and weak dimensions of rings and ring spectra (2009)
The primary object of this paper is to prove the conjecture of the authors from a previous paper, explaining how to recover the weak dimension of a ring from its derived category. In the process, we...
Model category structures on chain complexes of sheaves (2008)
of unbounded chain complexes, where the cofibrations are the injections. This folk theorem is apparently due to Joyal, and has been generalized recently
PHANTOM MAPS AND CHROMATIC PHANTOM MAPS (2008)
Abstract. In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all...
QUILLEN MODEL STRUCTURES FOR RELATIVE HOMOLOGICAL ALGEBRA (2008)
of the ring R. This example shows that traditional homological algebra is encompassed by Quillen’s homotopical algebra. The goal of this paper is to show that more general forms of homological...
Lusternik-Schnirelmann Cocategory (2008)
We introduce a new definition of the (Lusternik-Schnirelmann) cocategory of a CW complex X. This is accomplished by producing a dual of the fat wedge called the thin product. One then looks at...
Model category structures on chain complexes of sheaves (2007)
this model structure is not very useful for dening derived tensor products. We therefore consider another method for constructing a model structure, and apply it to the category of sheaves on a...
QUILLEN MODEL STRUCTURES FOR RELATIVE HOMOLOGICAL ALGEBRA (2007)
of the ring R. This example shows that traditional homological algebra is encompassed by Quillen's homotopical algebra. The goal of this paper is to show that more general forms of homological...
Karen L. Collins, Mark Hovey, Problem B
We give a bijective proof for the identity S(n; k) ( n j 1 n k) (mod 2) where j = b k
We extend the denition of edge-cordial graphs due to Ng and Lee for graphs on 4k, 4k+1, and 4k+3 vertices to include graphs on 4k+2 vertices, and show that, in fact, all graphs without isolated...
PHANTOM MAPS AND CHROMATIC PHANTOM MAPS (2007)
Abstract. In the rst part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or...
Triangulations of projective modules (2007)
Hovey, Mark, Lockridge, Keir H.
We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields...
Cotorsion pairs and model categories (2007)
This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6,...
The generating hypothesis in the derived category of a ring (2007)
Hovey, Mark, Lockridge, Keir, Puninski, Gena
We show that a strong form (the fully faithful version) of the generating hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von...
The generating hypothesis in the derived category of a ring (2006)
Hovey, Mark, Lockridge, Keir, Puninski, Gena
We show that a strong form (the fully faithful version) of the generating hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von...
On Freyd's generating hypothesis (2006)
Freyd's generating hypothesis in stable homotopy theory is revisited and new consequences and equivalent forms of it are derived. A surprising such consequence is that I, the Brown-Comenetz dual of...
Local cohomology of ${BP_{*}BP}$-comodules (2005)
Given a spectrum $X$, we construct a spectral sequence of $BP_{*}BP$-comodules that converges to $BP_{*}(L_{n}X)$, where $L_{n}X$ is the Bousfield localization of $X$ with respect to the...
Operations and co-operations in Morava {$E$}-theory (2004)
Let $E=E_{n}$ denote the Morava $E$-theory spectrum, and let $\Gamma$ be the Morava stabilizer group of ring spectrum isomorphisms of $E$. We revisit the isomorphism $\pi_{*}L_{K(n)}(E\smash E)\cong...
Homotopy theory of comodules over a Hopf algebroid (2003)
Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for...
Chromatic phenomena in the algebra of BP_{*}BP-comodules (2003)
This paper begins with an exposition of the author's research on the category of BP_*BP-comodules, much of which is joint with Neil Strickland. The main result of that work is that the category of...
Local cohomology of BP_*BP-comodules (2003)
In a previous paper, the authors showed that the category of E(n)_*E(n)-comodules is a localization of the category of BP_*BP-comodules. In this paper, we study the resulting localization functor L_n...
Comodules and Landweber exact homology theories (2003)
We show that, if E is a Landweber exact ring spectrum, then the category of E_*E-comodules is equivalent to the localization of the category of BP_*BP-comodules with respect to the hereditary torsion...
Morita theory for Hopf algebroids and presheaves of groupoids (2001)
Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff, the opposite category of...
Quillen model structures for relative homological algebra (2000)
Christensen, J. Daniel, Hovey, Mark
An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that...
Spectra and symmetric spectra in general model categories (2000)
(This is an updated version; following an idea of Voevodsky, we have strengthened our results so all of them apply to one form of motivic homotopy theory). We give two general constructions for the...
Classifying subcategories of modules (1999)
In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete...
Model category structures on chain complexes of sheaves (1999)
In this paper, we try to realize the unbounded derived category of an abelian category as the homotopy category of a Quillen model structure on the category of unbounded chain complexes. We construct...
Morava K-theories and localisation (1999)
Abstract. We study the structure of the categories of K(n)-local and E(n)local spectra, using the axiomatic framework developed in earlier work of the authors with John Palmieri. We classify...
Invertible Spectra In The E(n)-Local Stable Homotopy Category (1999)
this paper). Here the smash product of two E-local spectra need not be E-local, so one must relocalize the result by applying the Bousfield localization functor LE . The most well-known case is E =...
Phantom maps and chromatic phantom maps (1998)
Christensen, J. Daniel, Hovey, Mark
In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing...
Monoidal model categories (1998)
A monoidal model category is a model category with a compatible closed monoidal structure. Such things abound in nature; simplicial sets and chain complexes of abelian groups are examples. Given a...
The structure of the Bousfield lattice (1998)
Using Ohkawa's theorem that the collection of Bousfield classes is a set, we perform a number of constructions with Bousfield classes. In particular, we describe a greatest lower bound operator; we...
Hovey, Mark, Shipley, Brooke, Smith, Jeff
The long hunt for a symmetric monoidal category of spectra finally ended in success with the simultaneous discovery of the third author's discovery of symmetric spectra and the...
Mark Hovey, Brooke Shipley, Jeff Smith
this paper we study a particularly simple model for inverting such operations which preserves product structures. The combinatorial nature of this model means that it is easily transported, and hence...
Cohomological Bousfield Classes (1995)
this paper turn out in fact to be homological Bousfield classes, and thus have localization functors. We conjecture that every cohomological Bousfield class is a homological Bousfield class. The...
Cohomological Bousfield Classes (1995)
. In this paper, we begin the study of Bousfield classes for cohomology theories defined on spectra. Our main result is that a map f : X ! Y induces an isomorphism on E(n)-cohomology if and only if...
Tate Cohomology Lowers Chromatic Bousfield Classes (1994)
. Let G be a finite group. We use the results of [5] to show that the Tate homology of E(n) local spectra with respect to G produces E(n \Gamma 1) local spectra. We also show that the Bousfield class...
Bousfield localization functors and Hopkins' chromatic splitting conjecture (1993)
This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout
Bousfield Localization Functors and Hopkins' Chromatic Splitting Conjecture
This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local