Related papers: $\tau$-perpendicular wide subcategories

Let $k$ be a field and let $\Lambda$ be a finite dimensional $k$-algebra. We prove that every bounded complex $V^\bullet$ of finitely generated $\Lambda$-modules has a well-defined versal deformation ring $R(\Lambda,V^\bullet)$ which is a…

We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept "module (co)end". This tool allows us to give different proofs to several known results…

We study the maximal rigid subcategories in $2-$CY triangulated categories and their endomorphism algebras. Cluster tilting subcategories are obviously maximal rigid; we prove that the converse is true if the $2-$CY triangulated categories…

For some important families of complete infinite lattices, we study some generalizations of two fundamental notions which are mostly treated for finite lattices. Specifically, for well-separated $\kappa$-lattices, and also for weakly atomic…

We prove a model theoretic Baire category theorem for $\tilde\tau_{low}^f$-sets in a countable simple theory in which the extension property is first-order and show some of its applications. We also prove a trichotomy for minimal types in…

Let $\Lambda$ be a finite-dimensional algebra over a field $K$. We describe how Buan and Marsh's $\tau$-exceptional sequences can be used to give a "brick labeling" of a certain poset of wide subcategories of finitely-generated…

We discuss finiteness/infiniteness of $\tau$-tilting modules over tensor products of two symmetric algebras. As an application, we discuss that over block algebras of direct products of finite groups.

For any good tilting module $T$ over a ring $A$, there exists an $n$-symmetric subcategory $\mathscr{E}$ of a module category such that the derived category of the endomorphism ring of $T$ is a recollement of the derived categories of…

In this short paper we prove that a finite dimensional algebra is hereditary if and only if there is no loop in its ordinary quiver and every $\tau$-tilting module is tilting.

Let $\C$ be an $(n+2)$-angulated category with shift functor $\Sigma$ and $\X$ be a cluster-tilting subcategory of $\C$. Then we show that the quotient category $\C/\X$ is an $n$-abelian category. If $\C$ has a Serre functor, then $\C/\X$…

For a localization of a smooth proper category along a subcategory preserved by the Serre functor, we show that morphisms in Efimov's algebraizable categorical formal punctured neighborhood of infinity can be computed using the natural cone…

We give an example of a finite-dimensional algebra with a 2-cluster tilting module and a simple module which has infinite complexity. This answers a question of Erdmann and Holm.

In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…

For a finite-dimensional algebra $\Lambda$ over an algebraically closed field $K$, it is known that the poset of $2$-term silting objects in $\mathrm{K}^b(\operatorname{proj}\Lambda)$ is isomorphic to the poset of functorially finite…

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…

We show that the action of the Serre functor on the subcategory of projective-injective modules in a parabolic BGG category $\mathcal O$ of a quasi-reductive finite dimensional Lie superalgebra is given by tensoring with the top component…

Let $k$ be an algebraically closed field. Let $R$ be a finite dimensional commutative local $k$-algebra and let $Q$ be a quiver with no oriented cycles. In this paper, we study (signed) $\tau$-exceptional sequences over the algebra $\Lambda…

Let $\mathbb{X}$ be a weighted projective line and $\operatorname{coh}\mathbb{X}$ the associated categoy of coherent sheaves. We classify the tilting complexes $T$ in $D^b(\operatorname{coh}\mathbb{X})$ such that $\tau^2 T\cong T$, where…

For a (right and left) coherent ring $A$, we show that there exists a duality between homotopy categories ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A^{{\rm op}})$ and ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A)$. If $A=\Lambda$ is an…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…