From torsion theories to closure operators and factorization systems
Authors
Abstract:
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
similar resources
Fuzzy Closure Systems and Fuzzy Closure Operators
We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F (S) and F (C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.
full textn-closure systems and n-closure operators
It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices,...
full textFactorization, Fibration and Torsion
A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3–for–2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and of weak factorization system, as used in abstract homotopy theory.
full textSemi-abelian categories, torsion theories and factorisation systems
Semi-abelian categories [5] provide a suitable axiomatic context to study, among other things, the (co)homology of non-abelian algebraic structures (such as groups, compact groups, crossed modules, commutative rings, and Lie algebras), torsion and radical theories, and commutator theory. In this talk a brief introduction to some elementary properties of these categories will be given, before fo...
full textFinite and Torsion Kk-theories
We develop a finite KK-theory of C∗-algebras following ArlettazH.Inassaridze’s approach to finite algebraic K-theory [1] . The BrowderKaroubi-Lambre’s theorem on the orders of the elements for finite algebraic K-theory [ , ] is extended to finite KK-theory. A new bivariant theory, called torsion KK-theory is defined as the direct limit of finite KK-theories. Such bivariant K-theory has almost a...
full textClosure Operators and Subalgebras
In this article we present several logical schemes. The scheme SubrelstrEx concerns a non empty relational structure A, a set B, and a unary predicate P, and states that: There exists a non empty full strict relational substructure S of A such that for every element x of A holds x is an element of S if and only if P[x] provided the following conditions are met: • P[B], • B ∈ the carrier of A. T...
full textMy Resources
Journal title
volume 12 issue 1
pages 89- 121
publication date 2020-01-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023