The ideas behind splitting classes were introduced by Freyd and Scedrov in [1] and expanded by Lippincott in [2]. In the latter work, Lippincott proves that there are exactly six splitting class pairs in the category of sets, but uncountably many in the category of groups. In this paper, we prove much more generally that any category containing the category of finite abelian p-groups as a full ...

The present paper introduces aggregative spaces and their category AGS, and then establishes a dual adjunction between AGS and the category Agop of aggregation operators on bounded partially ordered sets. Spatial aggregation operators and sober aggregative spaces, enabling us to restrict the dual adjunction between AGS and Agop to a dual equivalence between the full subcategory of Agop consisti...

We show that the quotients of the continuous cluster category Cπ and the rational subcategory X modulo the additive subcategory generated by any cluster are abelian categories and we show that they are isomorphic to categories of infinite and finite length modules, respectively, over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-ChapotonSchiffler and Buan-M...

Let (R,m) be a commutative Noetherian local ring with m = (0). We give a condition for R to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of projective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over R is not necessarily a...

We show that the quotients of the continuous cluster category Cπ and the rational subcategory X modulo the additive subcategory generated by any cluster are abelian categories and we show that they are isomorphic to categories of infinite and finite length modules, respectively, over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-ChapotonSchiffler and Buan-M...

Let R be a commutative ring whose complete ring of quotients is Rinjective. We show that the category of topological R-modules contains a full subcategory that is ∗-autonomous using R itself as dualizing object. In order to do this, we develop a new variation on the category chu(D, R), where D is the category of discrete R-modules: the high wide subcategory, which we show equivalent to the cate...

Let G be a finite group and let k be a field whose characteristic p divides the order of G. Freyd’s generating hypothesis for the stable module category of G is the statement that a map between finite-dimensional kG-modules in the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. We show that if G has periodic cohomology then the gen...

It is well known that the category MC of right comodules over an A-coring C, A an associative ring, is a subcategory of the category of left modules ∗CM over the dual ring ∗C. The main purpose of this note is to show that MC is a full subcatgeory in ∗CM if and only if C is locally projective as a left A-module.