Coherence for rewriting 2-theories
Coherence for rewriting 2-theories
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重写 2 理论的连贯性
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J. Cohen
中科院分区：
文献类型：
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作者：
J. Cohen
一般的一致性定理的构造，产生明确的介绍范畴和代数对象。所涉及的范畴结构是有限离散的Lawvere 2-理论，尽管它们是在术语重写理论的语言中接近的。得到了两个广义相干定理。第一个适用于终止和合流重写2-理论。利用这一结果来构建系统的介绍，更高的汤普森集团和Higman-Thompson集团。的演示文稿是绝对有趣的，因为它们产生于更高的arity类似物的Stasheff/Mac巷的一致性公理，其中涉及的现象不存在于经典的二进制公理。第二个一般相干定理适用于不一定是汇合或终止的2-理论，并用于构造迭代monoidal范畴的相干性的新证明，迭代monoidal范畴作为迭代loop空间的范畴模型而出现，并且不汇合。
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language of term rewriting theory. Two general coherence theorems are obtained. The first applies to terminating and confluent rewriting 2-theories. This result is exploited to construct systematic presentations for the higher Thompson groups and the Higman-Thompson groups. The presentations are categorically interesting as they arise from higher-arity analogues of the Stasheff/Mac Lane coherence axioms, which involve phenomena not present in the classical binary axioms. The second general coherence theorem holds for 2-theories that are not necessarily confluent or terminating and is used to construct a new proof of coherence for iterated monoidal categories, which arise as categorical models of iterated loop spaces and fail to be confluent.
计算机科学中的代数和余代数
DOI：
10.1007/978-3-642-22944-2_7
发表时间：
2011
期刊：
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影响因子：
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作者：
Balan A
通讯作者：
Balan A