Traces for Coalgebraic Components.
Traces for Coalgebraic Components.
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代数分量的迹线。
DOI：
10.1017/s0960129510000551
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发表时间：
2011
影响因子：
0.5
通讯作者：
Ichiro Hasuo and Bart Jacobs
中科院分区：
文献类型：
--
作者：
Ichiro Hasuo;Kenta Cho;Toshiki Kataoka;and Bart Jacobs;Ryoichi Kobayashi;Ichiro Hasuo and Bart Jacobs
本文贡献的反馈算子，在一个monoidal跟踪的形式，理论的共代数，基于状态的组件建模。组件上的反馈算子满足Joyal，Street和Verity的迹公理。我们采用麦柯迪的管图，这是一个扩展的标准字符串图monoidal类别，表示和操纵组件图。微观世界原理然后产生一个典型的“内部”跟踪monoidal结构的范畴上的applications（最终coalgebras/组件的元素）。这概括了Abramsky，Haghverdi和Scott的观察。
This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, state-based modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy's tube diagrams, which are an extension of standard string diagrams for monoidal categories, to represent and manipulate component diagrams. The microcosm principle then yields a canonical ‘inner’ traced monoidal structure on the category of resumptions (elements of final coalgebras/components). This generalises an observation by Abramsky, Haghverdi and Scott.