Adjoint Relations Between the Category of Poset Acts and Some Other Categories

IF 0.7 Q2 MATHEMATICS

Tamkang Journal of Mathematics Pub Date : 2022-10-15 DOI:10.5556/j.tkjm.54.2023.4966

L. Shahbaz

引用次数: 1

Abstract

In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors between this category and the categories Pos-S of all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study the existence of their left and right adjoints. It is shown that the category Pos-S is a full reflective and coreflective subcategory of PosAct-S.

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后置行为范畴与其他范畴的伴随关系

在本文中，首先讨论了拟多项式S上所有偏序行为在postact -S范畴中的同余;在所有偏序集的po范畴中引入了一个s -行为，它们之间具有保持动作的单调映射。然后，我们研究了PosAct-S范畴中自由对象和共自由对象的存在性。更确切地说，我们考虑在这个范畴和所有s-偏集的po - s、所有偏集的po、所有s-偏集的Act-S和所有集合的Set范畴之间的所有遗忘函子，并研究它们的左右伴随的存在性。结果表明，post - s范畴是post - s的全反思性和共反思性子范畴。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Tamkang Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

期刊介绍： To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.

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