RANGE CATEGORIES I: GENERAL THEORY
RANGE CATEGORIES I: GENERAL THEORY
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范围类别 I：一般理论
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Pieter J. W. Hofstra
中科院分区：
文献类型：
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作者：
J. Cockett;Xiuzhan Guo;Pieter J. W. Hofstra
在这篇由两部分组成的论文中，我们对抽象部分地图类别进行了系统研究，其中每个地图都具有限制（定义域）和范围（图像）。在第一部分中，我们探讨了与逆范畴和寓言等相关结构的联系，并建立了两个代表性结果。第一个解释了如何将每个范围类别完全且忠实地嵌入到配备合适分解系统的部分地图类别中。第二个是鲍里斯·沙恩（Boris Schein）半群理论结果的概括，并表示满足每个映射都是其范围上的外同态这一附加条件的每个小范围范畴都可以忠实地嵌入到具有通常范围概念的集合和偏函数范畴中。最后，我们根据某些类型的标记树给出了部分地图类别上自由范围类别的显式构造。
In this two-part paper, we undertake a systematic study of abstract partial map categories in which every map has both a restriction (domain of definition) and a range (image). In this first part, we explore connections with related structures such as inverse categories and allegories, and establish two representational results. The first of these explains how every range category can be fully and faithfully embedded into a category of partial maps equipped with a suitable factorization system. The second is a generalization of a result from semigroup theory by Boris Schein, and says that every small range category satisfying the additional condition that every map is an epimorphism onto its range can be faithfully embedded into the category of sets and partial functions with the usual notion of range. Finally, we give an explicit construction of the free range category on a partial map category in terms of certain types of labeled trees.