On the maximal exact structure of an additive category
We prove that every additive category has a unique maximal exact structure in the sense of Quillen.
Wolfgang Rump (2011)
Fundamenta Mathematicae
We prove that every additive category has a unique maximal exact structure in the sense of Quillen.
Kato, Goro (1985/1986)
Portugaliae mathematica
Peter Strömbeck (1973)
Mathematica Scandinavica
S. Balcerzyk, Phan Chan, R. Kiełpiński (1976)
Fundamenta Mathematicae
Jing He, Yonggang Hu, Panyue Zhou (2024)
Czechoslovak Mathematical Journal
For an integer , we introduce a simultaneous generalization of -exact categories and -angulated categories, referred to as one-sided -suspended categories. Notably, one-sided -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their -angulated counterparts. Additionally, we present a method for constructing -angulated quotient categories from Frobenius -prile categories. Our results unify and extend...
Bruns, Winfried, Gubeladze, Joseph (2002)
Beiträge zur Algebra und Geometrie
Barr, Michael (2006)
Theory and Applications of Categories [electronic only]
R. El Harti (2004)
Extracta Mathematicae
L. Waelbroeck (1982)
Banach Center Publications
L. Waelbroeck (1982)
Banach Center Publications
Ferdinando Mora, Fulvio Mora (1982)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Irwin S. Pressman (1990)
Publicacions Matemàtiques
Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories...
Jian He, Jing He, Panyue Zhou (2023)
Czechoslovak Mathematical Journal
The aim of this article is to study the relative Auslander bijection in -exangulated categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.
Chaoling Huang, Kai Deng (2013)
Matematički Vesnik
Soud Khalifa Mohamed (2009)
Colloquium Mathematicae
We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].
Gran, Marino, Rosický, Jir̆í (2004)
Theory and Applications of Categories [electronic only]
S. Mantovani (1998)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Marco Grandis (1981)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Wolfgang Rump (2015)
Fundamenta Mathematicae
It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
Taylor, Paul (2002)
Theory and Applications of Categories [electronic only]