关于𝑄-TOP/(𝑌，)中注入物和注入壳的存在性

IF 0.6 Q3 MATHEMATICS

Categories and General Algebraic Structures with Applications Pub Date : 2022-07-01 DOI:10.52547/cgasa.2022.102640

Harshita Tiwari, R. Srivastava

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引用次数: 0

摘要

．本文在Cagliari和Mantovani的激励下，利用它们的𝑇0反射，我们获得了逗号类别𝑄- TOP /(𝑌，)中(𝑌，)是分层的𝑄-拓扑空间时的射射对象(关于𝑄-拓扑空间的𝑄- TOP类别中的嵌入类)的表征。进一步,我们已经证明对任何𝑄拓扑空间(𝑌𝜎)的存在的单射船体((𝑓𝑋𝜏))在逗号类别𝑄-前/(𝑌𝜎)相当于一个单射的存在船体的𝑇0反射((˜𝑋,˜𝜏),˜𝑓)逗号类𝑄-前/(˜𝑌,˜𝜎)(和逗号类别𝑄- 0 /(˜𝑌,˜𝜎),在𝑄-前表示一类𝑇0𝑄拓扑空间)。

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On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)

. In this paper, motivated by Cagliari and Mantovani, we have obtained a characterization of injective objects (with respect to the class of embeddings in the category 𝑄 - TOP of 𝑄 -topological spaces) in the comma category 𝑄 - TOP /( 𝑌, 𝜎 ) , when ( 𝑌, 𝜎 ) is a stratified 𝑄 -topological space, with the help of their 𝑇 0 -reflection. Further, we have proved that for any 𝑄 -topological space ( 𝑌, 𝜎 ) , the existence of an injective hull of (( 𝑋, 𝜏 ) , 𝑓 ) in the comma category 𝑄 - TOP /( 𝑌, 𝜎 ) is equivalent to the existence of an injective hull of its 𝑇 0 -reflection (( ˜ 𝑋, ˜ 𝜏 ) , ˜ 𝑓 ) in the comma category 𝑄 - TOP /( ˜ 𝑌, ˜ 𝜎 ) (and in the comma category 𝑄 - TOP 0 /( ˜ 𝑌, ˜ 𝜎 ) , where 𝑄 - TOP 0 denotes the category of 𝑇 0 - 𝑄 -topological spaces).

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来源期刊

Categories and General Algebraic Structures with Applications MATHEMATICS-

CiteScore

1.40

自引率

11.10%

发文量

审稿时长

8 weeks

期刊介绍： Categories and General Algebraic Structures with Applications is an international journal published by Shahid Beheshti University, Tehran, Iran, free of page charges. It publishes original high quality research papers and invited research and survey articles mainly in two subjects: Categories (algebraic, topological, and applications in mathematics and computer sciences) and General Algebraic Structures (not necessarily classical algebraic structures, but universal algebras such as algebras in categories, semigroups, their actions, automata, ordered algebraic structures, lattices (of any kind), quasigroups, hyper universal algebras, and their applications.