On the additive categories of generalized standard almost cyclic coherent Auslander–Reiten components

Generalized Singular Value Decomposition with Additive Components

The singular value decomposition (SVD) technique is extended to incorporate the additive components for approximation of a rectangular matrix by the outer products of vectors. While dual vectors of the regular SVD can be expressed one via linear transformation of the other, the modified SVD corresponds to the general linear transformation with the additive part. The method obtained can be relat...

Almost Complete Cluster Tilting Objects in Generalized Higher Cluster Categories

We study higher cluster tilting objects in generalized higher cluster categories arising from dg algebras of higher Calabi-Yau dimension. Taking advantage of silting mutations of Aihara-Iyama, we obtain a class of m-cluster tilting objects in generalized m-cluster categories. For generalized m-cluster categories arising from strongly (m + 2)-Calabi-Yau dg algebras, by using truncations of minim...

Inferences About the Components of a Generalized Additive Model

On the Cyclic Homology of Exact Categories

The cyclic homology of an exact category was defined by R. McCarthy [17] using the methods of F. Waldhausen [26]. McCarthy’s theory enjoys a number of desirable properties, the most basic being the extension property, i.e. the fact that when applied to the category of finitely generated projective modules over an algebra it specializes to the cyclic homology of the algebra. However, we show tha...

Categories of imaginaries for definable additive categories

An additive category is definable if it is equivalent to a definable subcategory of a module category Mod-R, meaning a full subcategory which is closed under direct products, direct limits (= directed colimits) and pure subobjects. Such a category D has associated to it a canonical model theory for its objects in the sense that each object D ∈ D becomes a structure for the associated language; ...