Symmetric monoidal sketches
Symmetric monoidal sketches
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对称幺半群草图
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
J. Power
中科院分区：
文献类型：
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作者：
M. Hyland;J. Power
我们引进并发展了对称幺半群的概念。每一个对称的monoidal草图生成一个通用模型。如果草图是可交换的和单排序的，则类属模型可以被表征为小类别1上的自由结构类别。此外，在小对称monoidal范畴和严格对称monoidal函子的范畴SymMons上存在一个共单Mods（S，−），使得Mods（S，−）-余代数范畴描述了上述结构。给定一个交换单序草图，将一个小的对称么半群范畴发送到其中草图的模型范畴的构造提供了从余代数范畴到SymMons的遗忘函子的右伴随。我们调查的Eckmann-Hilton参数，它允许一个简单的表征的建设所产生的具体情况。这说明了目前正在研究的各种类别的布线建模并发，以及为理解公理域理论和并发的预层模型中的公理生成的类别提供了基础。
We introduce and develop the notion of symmetric monoidal sketch. Every symmetric monoidal sketch generates a generic model. If the sketch is commutative and single-sorted, the generic model can be characterised as a free structured category on the small category 1. Moreover, there is a comonad Mods(S,−) on the category SymMons of small symmetric monoidal categories and strict symmetric monoidal functors such that the category of Mods(S,−)-coalgebras describes the above-mentioned structure. Given a commutative single-sorted sketch, the construction sending a small symmetric monoidal category to the category of models of the sketch in it provides a right adjoint to the forgetful functor from the category of coalgebras to SymMons. We investigate specific cases generated by the Eckmann-Hilton argument, which allows a simple characterisation of the constructions. This accounts for the various categories of wiring currently being investigated in modelling concurrency, as well as providing a basis for understanding the axiomatically generated categories in axiomatic domain theory and in presheaf models of concurrency.