O. Mendoza

activity

20072023

most citedFrobenius pairs in abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts

27 citations · 55 across the 18 of their papers we have counts for

collaborators

24 papers

math.RT2023

Quotient categories with exact structure from $(n + 2)$ -rigid subcategories in extriangulated categories

Mindy Y. Huerta, Octavio Mendoza, Corina Sáenz +1

In this work we introduce the notion of higher $E$ -extension groups for an extriangulated category $C$ and study the quotients $\mathcal{X}_{n+1}^{\vee}/[\mathca…

math.CT2022

Cut notions in extriangulated categories related to Auslander-Buchweitz theory and cotorsion theory

Mindy Huerta, Octavio Mendoza, Corina Sáenz +1

In this work we introduce notions in Auslander-Buchweitz theory and cotorsion theory in extriangulated categories which extend the given ones for abelian categories. Although these…

math.RA2022

$m$ -periodic Gorenstein objects

Mindy Huerta, Octavio Mendoza, Marco A. Pérez

We present and study the concept of $m$ -periodic Gorenstein objects relative to a pair $(A, B)$ of classes of objects in an abelian category, as a generalization of $m$ -st…

math.RT2022

$n$ -term silting complexes in $K^{b} (p r o j (Λ))$

Luis Martinez, Octavio Mendoza

Let $Λ$ be an Artin algebra and $K^{b} (p r o j (Λ))$ be the triangulated category of bounded co-chain complexes in $p r o j (Λ) .$ It is well known that two-terms silting complexes in $K^b(pr…

math.CT2022

Balanced systems for $Hom$

Víctor Becerril, Octavio Mendoza, Marco A. Pérez

From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(X, ω); (ν, Y)]$ as a tool to induce balan…

math.RT2021

Relative Torsion Classes, relative tilting and relative silting modules

Luis Martínez, Octavio Mendoza

Let $Λ$ be an Artin algebra. In 2014, T. Adachi, O. Iyama and I. Reiten proved that the torsion funtorially finite classes in $mod (Λ)$ can be described by the $τ$ -tiltin…

math.RA2021★ 1 cited

Standardly stratified lower triangular $K$ -algebras with enough idempotents

E. Marcos, O. Mendoza, C. Sáenz +1

In this paper we study the lower triangular matrix $K$ -algebra $Λ := [T M 0 U],$ where $U$ and $T$ are basic $\mathbb…

math.CT2020★ 3 cited

Cut cotorsion pairs

Mindy Huerta, Octavio Mendoza, Marco A. Pérez

We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general frame…

math.RT2020

Generalised Igusa-Todorov functions and Lat-Igusa-Todorov algebras

Diego Bravo, Marcelo Lanzilotta, Octavio Mendoza +1

In this paper we study a generalisation of the Igusa-Todorov functions which gives rise to a vast class of algebras satisfying the finitistic dimension conjecture. This class of al…

math.RT2019

Stratifying systems through $τ$ -tilting theory

Octavio Mendoza, Hipolito Treffinger

In this paper we first show that every non-zero $τ$ -rigid $A$ -module induces at least one stratifying system in the module category of $A$ . Moreover, we show that each of these str…

math.RT2019★ 9 cited

$n$ -Cotorsion pairs

Mindy Huerta, Octavio Mendoza, Marco A. Pérez

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective modules over an Iwanaga-Gorenstein ring, we present the concept of left and right $n$ -cotor…

math.RA2018

Relative Gorenstein objects in abelian categories

Victor Becerril, Octavio Mendoza, Valente Santiago

Let $A$ be an abelian category. For a pair $(X, Y$ of classes of objects in $A,$ we define the weak and the $(X, Y)$ -Goren…

math.RT2018

Cokernels of the Cartan Matrix and Stratifying Systems

Eduardo Marcos, Octavio Mendoza, Corina Sáenz

We study the cokernel of the application given by the Cartan Matrix $C_{Λ}$ of a finite dimensional $k$ -algebra $Λ.$ This produces a finitely generated abelian group, the Cartan grou…

math.RT2018

Pullback diagrams, syzygy finite classes and Igusa-Todorov algebras

Diego Bravo, Marcelo Lanzilotta, Octavio Mendoza

For an abelian category $A$ , we define the category PEx( $A$ ) of pullback diagrams of short exact sequences in $A$ , as a subcategory of the functor cat…

math.RA2018

A generalization of the theory of standardly stratified algebras I: Standardly stratified ringoids

O. Mendoza, M. Ortíz, C. Sáenz +1

We extend the classical notion of standardly stratified $k$ -algebra (stated for finite dimensional $k$ -algebras) to the more general class of rings, possibly without $1,$ with enou…

math.RA2016

Relative Igusa-Todorov functions and relative homological dimensions

Marcelo Lanzilotta, Octavio Mendoza

We develope the theory of the $E$ -relative Igusa-Todorov functions in an exact $I T$ -context $(C, E) .$ In the case when $C =$ mod $(Λ)$ is th…

math.CT2016★ 27 cited

Frobenius pairs in abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts

Víctor Becerril, Octavio Mendoza Hernandez, Marco A. Pérez +1

In this work, we revisit Auslander-Buchweitz Approximation Theory and find some relations with cotorsion pairs and model category structures. From the notions of relatives generato…

math.RA2016★ 1 cited

Coherent subcategories of finitely generated $Λ$ -modules

E. N. Marcos, O. Mendoza, C. Sáenz +1

We explore some properties of wide subcategories of the category mod $(Λ)$ of finitely generated left $Λ$ -modules, for some artin algebra $Λ.$ In particular we look at wide finite…

math.CT2013

Homological systems in triangulated categories

Octavio Mendoza, Valente Santiago

We introduce the notion of homological systems $Θ$ for triangulated categories. Homological systems generalize, on one hand, the notion of stratifying systems in module categories,…

math.RT2013

Split-by-nilpotent extensions algebras and stratifying systems

Marcelo Lanzilotta, Octavio Mendoza, Corina Sáenz

Let $Γ$ and $Λ$ be artin algebras such that $Γ$ is a split-by-nilpotent extension of $Λ$ by a two sided ideal $I$ of $Γ.$ Consider the so-called change of rings functors $G:={}_ΓΓ_…

math.RT2013★ 1 cited

The Phi-dimension: A new homological measure

Sonia Fernandes, Marcelo Lanzilotta, Octavio Mendoza

K. Igusa and G. Todorov introduced two functions $ϕ$ and $ψ,$ which are natural and important homological measures generalising the notion of the projective dimension. These Igusa-…

math.CT2010★ 13 cited

Auslander-Buchweitz approximation theory for triangulated categories

O. Mendoza, E. C. Saenz, V. Santiago +1

We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homo…

math.RT2007

An approach to the finitistic dimension conjecture

François Huard, Octavio Mendoza, Marcelo Lanzilotta

Let $R$ be a finite dimensional $k$ -algebra over an algebraically closed field $k$ and $mod R$ be the category of all finitely generated left $R$ -modules. For a given full…

math.RT2007

Finitistic dimension through infinite projective dimension

Francois Huard, Marcelo Lanzilotta, Octavio Mendoza

We show that an artin algebra having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with…

Quotient categories with exact structure from (n+2)-rigid subcategories in extriangulated categories

Cut notions in extriangulated categories related to Auslander-Buchweitz theory and cotorsion theory

m-periodic Gorenstein objects

n-term silting complexes in Kb(proj(Λ))

Balanced systems for Hom

Relative Torsion Classes, relative tilting and relative silting modules

Standardly stratified lower triangular K-algebras with enough idempotents

Cut cotorsion pairs

Generalised Igusa-Todorov functions and Lat-Igusa-Todorov algebras

Stratifying systems through τ-tilting theory

n-Cotorsion pairs

Relative Gorenstein objects in abelian categories

Cokernels of the Cartan Matrix and Stratifying Systems

Pullback diagrams, syzygy finite classes and Igusa-Todorov algebras

A generalization of the theory of standardly stratified algebras I: Standardly stratified ringoids

Relative Igusa-Todorov functions and relative homological dimensions

Frobenius pairs in abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts

Coherent subcategories of finitely generated Λ-modules

Homological systems in triangulated categories

Split-by-nilpotent extensions algebras and stratifying systems

The Phi-dimension: A new homological measure

Auslander-Buchweitz approximation theory for triangulated categories

An approach to the finitistic dimension conjecture

Finitistic dimension through infinite projective dimension

Quotient categories with exact structure from $(n + 2)$ -rigid subcategories in extriangulated categories

$m$ -periodic Gorenstein objects

$n$ -term silting complexes in $K^{b} (p r o j (Λ))$

Balanced systems for $Hom$

Standardly stratified lower triangular $K$ -algebras with enough idempotents

Stratifying systems through $τ$ -tilting theory

$n$ -Cotorsion pairs

Coherent subcategories of finitely generated $Λ$ -modules