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Clerc, F. Mimram, S.

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by the means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the objects are considered modulo an equivalence relation (in the spirit of rewriting modulo), whic...

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...

Paul Smith, S.
Published in
Advances in Mathematics

Let Q be a finite quiver with vertex set I and arrow set Q1, k a field, and kQ its path algebra with its standard grading. This paper proves some category equivalences involving the quotient category QGr(kQ)≔Gr(kQ)/Fdim(kQ) of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, namely QGr(kQ)≡ModS(Q)≡GrL(Q∘)≡ModL...

Rump, Wolfgang
Published in
Archiv der Mathematik

We introduce one-sided thick subcategories \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathcal{C}}$$ \end{document} of an arbitrary preadditive category \documen...

Walker, C. L.
Published in
Soft Computing

In this paper we look at two categories, the category ℱ of fuzzy subsets and a quotient category ℱ/ℳ of fuzzy sets. The category ℱ/ℳ is an extension of the category of sets, and the standard constructions in fuzzy set theory arise naturally within this category.