Related papers: Categorical Realizations of Quivers

Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…

We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are due to Joyal, Espan\~ol and the authors. We show that this gives a constructive…

We develop the theory of 2-quivers and quiver 2-categories to run in parallel with the classical theory of quiver algebras. A quiver 2-category is always finitary, and, conversely, every finitary 2-category will be bi-equivalent with a…

We prove that the category of graded finitely generated representations of the the cyclotomic quiver Schur algebra is a Koszul category.

We prove existence results for small presentations of model categories generalizing a theorem of D. Dugger from combinatorial model categories to more general model categories. Some of these results are shown under the assumption of…

In this paper, we develop a covering theory for the fractional Brauer configurations and connect it with the coverings of the associated quivers with relations in the sense of Mart\'inez-Villa and de la Pe\~na. Among the results, we show…

In this paper, we give a method for relating the generalized category $\mathcal{O}$ defined by the author and collaborators to explicit finitely presented algebras, and apply this to quiver varieties. This allows us to describe…

We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.

We show that if a connected, Hom-finite, Krull-Schmidt triangulated category has an Auslander-Reiten quiver component with Dynkin tree class then the category has Auslander-Reiten triangles and that component is the entire quiver. This is…

The singular cubical homology theory for the category of quivers or digraphs can be constructed similarly to the classical singular homology theory for topological spaces. The case of digraphs and quivers differs from the topological case…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…

We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $C_Q^{(t)}$ $(t=1,2,3)$, $\mathscr{C}_{\mathscr{Q}}^{(1)}$ and…

We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several…

One can regard the category of represenations of quivers in Hilbert spaces as a subcategory in the category of all representations, and at that objects, which are indecomposable in the subcategory, become in general decomposable in the…

Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition theorems for thick subcategories of various triangulated categories including the derived categories of rings, Noetherian stable homotopy categories, stable module…

We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved…

We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First we show that representation embeddings between categories of modules of finite-dimensional algebras induce embeddings of…

This expository article sets forth a self-contained and purely algebraic proof of a deep result of Quillen stating that the category of simplicial commutative algebras over a commutative ring is a model category. This is accomplished by…