有序集合的松弛逗号范畴

IF 0.6 4区数学 Q3 MATHEMATICS

Quaestiones Mathematicae Pub Date : 2023-11-01 DOI:10.2989/16073606.2023.2247729

Maria Manuel Clementino, Fernando Lucatelli Nunes

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引用次数: 0

摘要

摘要设Ord为(预)序集的范畴。不像Ord/X，它的行为是众所周知的，在文献中很少能找到关于松散的逗号2类Ord//X。本文证明遗忘函子Ord//X→Ord是拓扑的当且仅当X是完全的。并且，在适当的假设下，当且仅当X为时，Ord//X是完备且笛卡尔闭的。最后，我们分析这一类的血统。即，当X完备时，我们证明了对于Ord//X中的态射，在Ord//X中有效下降是充分条件，而在Ord//X中有效下降是必要条件。数学学科分类(2020):06a0718a2518a3018n1018d2018e50关键词:有效下降态，X, 2-范畴，逗号范畴，可指数性，笛卡尔闭范畴，拓扑函数，富范畴，富范畴

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Lax comma categories of ordered sets

AbstractLet Ord be the category of (pre)ordered sets. Unlike Ord/X , whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category Ord//X . In this paper we show that the forgetful functor Ord//X → Ord is topological if and only if X is complete. Moreover, under suitable hypothesis, Ord//X is complete and cartesian closed if and only if X is. We end by analysing descent in this category. Namely, when X is complete, we show that, for a morphism in Ord//X , being pointwise effective for descent in Ord is sufficient, while being effective for descent in Ord is necessary, to be effective for descent in Ord//X .Mathematics Subject Classification (2020): 06A0718A2518A3018N1018D2018E50Key words: Effective descent morphismslax comma 2-categoriescomma categoriesexponentiabilitycartesian closed categoriestopological functorsenriched categoriesOrd-enriched categories

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来源期刊

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.