Iterated distributive laws
Iterated distributive laws
复制标题
迭代分配律
DOI：
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发表时间：
2007
影响因子：
0.8
通讯作者：
Eugenia Cheng
中科院分区：
文献类型：
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作者：
Eugenia Cheng
本文给出了一个通过满足Yang-Baxter方程的分配律组合同一范畴上n个单子的框架，推广了Beck通过一个分配律组合两个单子的经典结果。我们表明，这对应于迭代n次的过程中采取的2类单子在2类，扩展的结果街特征分配律。我们表明，这个框架可以用来构建自由严格的n-范畴单子的n维球集，我们首先为每个i构造一个单子的组成沿着绑定i细胞，然后我们表明，这些单子之间的交换律定义分配律，满足必要的杨巴克斯特方程。
Abstract We give a framework for combining n monads on the same category via distributive laws satisfying Yang–Baxter equations, extending the classical result of Beck which combines two monads via one distributive law. We show that this corresponds to iterating n-times the process of taking the 2-category of monads in a 2-category, extending the result of Street characterising distributive laws. We show that this framework can be used to construct the free strict n-category monad on n-dimensional globular sets; we first construct for each i a monad for composition along bounding i-cells, and then we show that the interchange laws define distributive laws between these monads, satisfying the necessary Yang–Baxter equations.