Lucyshyn-Wright, Rory B. B.
Published in
Applied Categorical Structures

Certain axiomatic notions of affine space over a ring and convex space over a preordered ring are examples of the notion of T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docume...

Crivei, Septimiu
Published in
Results in Mathematics

We introduce weakly FP-injective and weakly flat functors, and we show that a right R-module K is FP-injective if and only if (−,K) is a flat weakly FP-injective functor in ((mod-R)op,Ab)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepa...

Gratz, Sira
Published in
Mathematische Zeitschrift

We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted cluster algebras of finite rank. Our framework is the category of rooted cluster algebras as introduced by Assem, Dupont and Schiffler. Relying on the proof of the po...

Coecke, Bob Heunen, Chris Kissinger, Aleks
Published in
Quantum Information Processing

We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of finite-dimensional C*-algebras and completely positive maps. In particular, the new category contains both quantu...

Liu, Jichun Sun, Longgang
Published in
Czechoslovak Mathematical Journal

A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We the...

Pogorzały, Zygmunt
Published in
Open Mathematics

In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.

Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A=kQ/I. Let QGrA denote the quotient of the category of graded right A-modules modulo the Serre subcategory consisting of those graded mo...

Adachi, Takanori

Kriz, Igor Pultr, Aleš
Published in
Applied Categorical Structures

The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article (Segal, Bull Am Math Soc 71:419–489, 1965). In our paper we follow his ideas from a different perspe...

Wehrung, Friedrich
Published in
Algebras and Representation Theory

The assignment (nonstable K0-theory), that to a ring R associates the monoid V( R ) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: There is no functor Γ, from simplicial monoids with order-...