Partially traced categories
Partially traced categories
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部分追踪类别
DOI：
10.1016/j.jpaa.2012.03.026
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
P. Selinger
中科院分区：
文献类型：
--
作者：
Octavio Malherbe;P. Scott;P. Selinger
本文涉及的问题有关Haghverdi和斯科特的概念部分跟踪类别。主要结果是这样的范畴的表示定理：我们证明了每一个部分跟踪范畴可以忠实地嵌入到一个完全跟踪的范畴。同样反过来，全迹范畴的每个对称么半群子范畴都是部分迹的，所以这完全刻画了部分迹范畴。我们使用的主要技术是基于Freyd的paracategories，沿着Joyal，Street和Verity的Int-construction的部分版本。
This paper deals with questions relating to Haghverdi and Scott’s notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced category can be faithfully embedded in a totally traced category. Also conversely, every symmetric monoidal subcategory of a totally traced category is partially traced, so this characterizes the partially traced categories completely. The main technique we use is based on Freyd’s paracategories, along with a partial version of Joyal, Street, and Verity’s Int-construction.