4 citations · 6 across the 6 of their papers we have counts for
7 papers
Triangular Matrix Categories over path Categories and Quasi-hereditary Categories, as well as one point extensions by Projectives
M. Ortiz-Morales, Rafael Ochoa
In this paper, we prove that the lower triangular matrix category , where and…
Gabriel localization in functor categories
Martin Ortiz-Morales, Martha Lizbeth Shaid Sandoval-Miranda, Valente Santiago-Vargas
P. Gabriel showed that for an unital ring , there exists a bijective correspondence between the set of Gabriel filters of and the set of Giraud subcategories of $\mathrm{Mod…
Triangular Matrix Categories I: Dualizing Varieties and generalized one-point extension
Alicia León-Galeana, Martín Ortiz-Morales, Valente Santiago Vargas
Following Mitchell's philosophy, in this paper we define the analogous of the triangular matrix algebra to the context of rings with several objects. Given two additive categories…
The Auslander-Reiten components seen as Quasi-hereditary Categories
M. Ortiz-Morales
Quasi-hereditary were introduced by L. Scott \cite{Scott, CPS1,CPS2} in order to deal highest weight categories as they arise in the representation theory of semi-simple complex Li…
Llinear Filters and Hereditary Torsion Theories in Functor Categories
M. Ortiz-Morales, S. Diaz-Alvarado
We introduce the notion of Gabriel filter for a preadditive category C and we show that there is a bijective correspondence between Gabriel filters of C and hereditary torsion theo…
Tilting theory and functor categories I. Classical tilting
R. Martínez-Villa, M. Ortiz-Morales
Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mat…
Tilting Theory and Functor Categories III. The Maps Category
R. Martinez-Villa, M. Ortiz-Morales
In this paper we continue the project of generalizing tilting theory to the category of contravariant functors , from a skeletally small preadditive category to the cat…