We investigate the triangulated hull of orbit categories perfect derived category and bounded a ring concerning power suspension functor. It turns out that will correspond to full subcategory compact objects certain periodic complexes. This specializes Stai Zhao's result when is finite dimensional algebra with global dimension over field. As first application, if $A,B$ are flat algebras commuta...

Abstract Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems have been proven in entirely abstract categorical terms. Closely related to categories are gs-monoidal also known as CD categories. These omit a condition that implements normalization probability. Extending work Corradini and Gadducci, we c...

We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg-Moore category of algebras over a suitable monad. This also suggests using monads directly, and our monadic approach to Galois desce...

Let D1, D2, D be non empty sets and let x be an element of [: [:D1, D2 :], D :]. Then x1,1 is an element of D1. Then x1,2 is an element of D2. Let D1, D2 be non empty sets and let x be an element of [:D1, D2 :]. Then x2 is an element of D2. Next we state the proposition (1) Let C, D be category structures. Suppose the category structure of C = the category structure of D. If C is category-like,...

Herschend-Liu-Nakaoka introduced the notion of n -exangulated categories. It is not only a higher dimensional analogue extriangulated categories defined by Nakaoka-Palu, but also gives simultaneous generalization -exact in sense Jasso and ( + 2 ) -angulated Geiss-Keller-Oppermann. Let C be an category with enough projectives injectives, X cluster tilting subcategory . In this article, we show t...

‎Based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified Polak-Ribière-Polyak conjugate‎ ‎gradient method proposed by Yu et al‎. ‎is presented‎.

We show that the gluing construction for Hilbert modules introduced by Raeburn in his computation of Picard group a continuous-trace C⁎-algebra (1981) [14] can be applied to arbitrary C⁎-algebras, via an algebraic argument with Haagerup tensor product. put this result into context descent theory identifying categories data over C⁎-algebras comodules C⁎-coalgebras, giving Hilbert-module version ...