We show that the homotopy category of complexes K(B) over any finitely accessible additive category B is locally well generated. That is, any localizing subcategory L in K(B) which is generated by a set is well generated in the sense of Neeman. We also show that K(B) itself being well generated is equivalent to B being pure semisimple, a concept which naturally generalizes right pure semisimpli...

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 demonstrate that commutativity of numerous one-dimensional subalgebras in W1+∞ algebra, i.e. the existence many non-trivial integrable systems described recent arXiv:2303.05273 follows from subset relations algebra known as Serre relations. No other are needed for commutativity. The survive deformation to affine Yangian Y(glˆ1), hence commutative do well. A special case parameters correspond...

We study relations between the Serre dimension defined as growth of entropy functor and global Bridgeland stability conditions due to Ikeda–Qiu. A fundamental inequality infimum dimensions is proved. Moreover, we characterize Gepner type on fractional Calabi–Yau categories via dimension, classify triangulated lower than one with a condition.

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...