Related papers: The singular Yoneda category and the stabilization…

Let $\Lambda$ be an Artin algebra and let $e$ be an idempotent in $\Lambda$. We study certain functors which preserve the singularity categories. Suppose $\mathrm{pd}\Lambda e_{e\Lambda e}<\infty$ and…

Let $X$ be a chain complex over a commutative noetherian ring $R$, that is, an object in the derived category $\mathcal{D}(R)$. We investigate the small support and co-support of $X$, introduced by Foxby and Benson, Iyengar, and Krause. We…

For a locally finitely presented Grothendieck category $\mathcal{A}$, we consider a certain subcategory of the homotopy category of FP-injective objects in $\mathcal{A}$ which we show is compactly generated. In the case where $\mathcal{A}$…

Let $kG$ be the group algebra of a finite group scheme defined over a field $k$ of characteristic $p>0$. Associated to any closed subset $V$ of the projectivized prime ideal spectrum $\operatorname{Proj} \operatorname{H}^*(G,k)$ is a thick…

This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…

Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…

The tube category of a modular tensor category is a variant of the tube algebra, first introduced by Ocneanu. As a category, it can be decomposed in two different, but related, senses. Firstly, via the Yoneda embedding, the Hom spaces…

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit S forms a commutative ring. An idempotent e of this ring will split the homotopy category. We prove that provided the…

We show that, for a right exact functor from an abelian category to abelian groups, Yoneda's isomorphism commutes with homology and, hence, with functor derivation. Then we extend this result to semiabelian domains. An interpretation in…

We extend the support theory of Benson--Iyengar--Krause to the non-Noetherian setting by introducing a new notion of small support for modules. This enables us to prove that the stable module category of a finite group is canonically…

We introduce a category of possibly irregular holonomic D-modules which can be endowed in a canonical way with an irregular Hodge filtration. Mixed Hodge modules with their Hodge filtration naturally belong to this category, as well as…

We study the category of discrete modules over the ring of degree zero stable operations in p-local complex K-theory. We show that the p-local K-homology of any space or spectrum is such a module, and that this category is isomorphic to a…

An $F$-nilpotent local ring is a local ring $(R, \mathfrak{m})$ of prime characteristic defined by the nilpotence of the Frobenius action on its local cohomology modules $H^i_{\mathfrak{m}}(R)$. A singularity in characteristic zero is said…

The center $Z(\mathcal{A})$ of an abelian category $\mathcal{A}$ is the endomorphism ring of the identity functor on that category. A localizing subcategory of a Grothendieck category $\mathcal{C}$ is said to be stable if it is stable under…

Let $(S, \n)$ be a commutative noetherian local ring and $\omega\in\n$ be non-zerodivisor. This paper deals with the behavior of the category $\mon(\omega, \cp)$ consisting of all monomorphisms between finitely generated projective…

We consider a closed symmetric monoidal category $\mathcal{M}$. We show that if $I$ is a small category then $\mathcal{M}^I$ is a closed $\mathcal{M}$-module. We rewrite the Yoneda Lemma in the case of monoidal valued functors. We derive an…

It is known that the Grothendieck group of the category of Schur functors is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a "plethory": a monoid in the category of…

We introduce the compactness locus of a geometric functor between rigidly-compactly generated tensor-triangulated categories, and describe it for several examples arising in equivariant homotopy theory and algebraic geometry. It is a subset…

We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also…