Related papers: The stable module category and model structures fo…
The extriangulated category is a simultaneous generalization of exact categories and triangulated categories. H. Nakaoka and Y. Palu have proved that the homotopy category of an admissible model structure on a weakly idempotent complete…
For a category $\mathcal E$ with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simplicial objects in $\mathcal E$, generalising the Kan--Quillen…
This chapter, written for "Stable categories and structured ring spectra," edited by Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill, surveys the history of homotopical categories, from Gabriel and Zisman's categories of fractions…
The existence of a model structure on the category $\mathcal{D}$ of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model structure on the category $\mathcal{D}$ whose weak…
We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion…
Considering the monoidal category $\mathcal{C}$ obtained as modules over a Hopf algebra $H$ in a rigid braided category $\mathcal{B}$, we prove decomposition results for the Hochschild and cyclic homology categories $HH(\mathcal{C})$ and…
We introduce the notion of $\pi$-cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories.…
Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous $G$-modules for a Hausdorff topological group $G$. We study the resulting notion of group cohomology and its…
Building on work of Marta Bunge in the one-categorical case, we characterize when a given model category is Quillen equivalent to a presheaf category with the projective model structure. This involves introducing a notion of homotopy atoms,…
We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…
This is a continuation of the paper "Modular tensor categories and orbifold theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal filed theory, or, in mathematical language, question of constructing the category of…
For any dg algebra $A$ we construct a closed model category structure on dg $A$-modules such that the corresponding homotopy category is compactly generated by dg $A$-modules that are finitely generated and free over $A$ (disregarding the…
Let $G$ be an infinite discrete group. A classifying space for proper actions of $G$ is a proper $G$-CW-complex $X$ such that the fixed point sets $X^H$ are contractible for all finite subgroups $H$ of $G$. In this paper we consider the…
In this paper, we plan to build upon significant results by Amnon Neeman regarding the homotopy category of flat modules to study ${\mathbb{K}}({S\rm{SF}}\mbox{-}R)$, the homotopy category of $S$-strongly flat modules, where $S$ is a…
The (co)completeness problem for the (projectively) stable module category of an associative ring is studied. (Normal) monomorphisms and (normal) epimorphisms in such a category are characterized. As an application, we give a criterion for…
Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied…
We generalize Quillen's $F$-isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of…
We study induced model structures on Frobenius categories. In particular we consider the case where $\mathcal{C}$ is the category of comodules of a supercommutative Hopf algebra $A$ over a field $k$. Given a graded Hopf algebra quotient $A…
We prove two results from Morita theory of stable model categories. Both can be regarded as topological versions of recent algebraic theorems. One is on recollements of triangulated categories, which have been studied in the algebraic case…
We show that the category of N-complexes has a Str\om model structure, meaning the weak equivalences are the chain homotopy equivalences. This generalizes the analogous result for the category of chain complexes (N = 2). The trivial objects…