Topogenous orders and related families of morphisms

IF 0.6 4区 数学 Q3 MATHEMATICS
David Holgate, Minani Iragi
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引用次数: 0

Abstract

AbstractIn a category with a proper ()-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow simultaneous study of four classes of morphisms obtained separately with respect to closure, interior and neighbourhood operators, the initial and final morphisms lead us to the study of topogenous orders induced by pointed and co-pointed endofunctors. We also lift the topogenous orders along an -fibration. This permits one to obtain the lifting of interior and neighbourhood operators along an -fibration and includes the lifting of closure operators found in the literature. A number of examples presented at the end of the paper demonstrates our results.Mathematics Subject Classification (2020): 18A0518F6054A1554B30Key words: Closure operatorinterior operatorcategorical topogenous orderheredity(co)pointed endofunctors-fibrationsstrict, co-strictinitial and final morphisms
形态变异的拓扑目和相关科
摘要在具有适当分解系统的范畴中,研究了拓扑序的严格态射、共严格态射、初态射和终态射的概念。除了表明它们允许同时研究关于闭包算子、内算子和邻域算子分别获得的四类态射外,初始态射和最终态射还引导我们研究由点和共点内函子诱导的拓扑序。我们还沿着一条-纤颤线提升了地形秩序。这允许人们获得沿-振动的内部算子和邻域算子的提升,并包括文献中发现的闭包算子的提升。文章最后给出了一些例子,证明了我们的结果。数学学科分类(2020):18a0518f6054a1554b30关键词:闭包算子;内算子;分类拓扑有序遗传(co)点内函子
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来源期刊
Quaestiones Mathematicae
Quaestiones Mathematicae 数学-数学
CiteScore
1.70
自引率
0.00%
发文量
121
审稿时长
>12 weeks
期刊介绍: Quaestiones Mathematicae is devoted to research articles from a wide range of mathematical areas. Longer expository papers of exceptional quality are also considered. Published in English, the journal receives contributions from authors around the globe and serves as an important reference source for anyone interested in mathematics.
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