乘法范畴结合性的一致性
Coherence of Associativity in Categories with Multiplication
摘要：
MacLane关于乘法范畴的通常的凝聚定理假设某个五边形图交换，以得出结合性同构在某种实际意义上是良好定义的结论。实践方面包括创建结合同构从一个给定的张量与单位的权利或左。我们表明，通过重新检查麦克莱恩的原始参数，如果张量与身份被限制在一边，那么良好的定义构造同构遵循自然性只，没有必要的交换性的五边形图。这一观察结果是通过注意到通常的相干定理与称为汤普森群F的非对称群的某些性质的相似性而发现的。这份报纸将被视为这种联系的广告。
英文摘要：
The usual coherence theorem of MacLane for categories with multiplication assumes that a certain pentagonal diagram commutes in order to conclude that associativity isomorphisms are well defined in a certain practical sense. The practical aspects include creating associativity isomorphisms from a given one by tensoring with the identity on either the right or the left. We show, by reinspecting MacLane's original arguments, that if tensoring with the identity is restricted to one side, then the well definedness of constructed isomorphisms follows from naturality only, with no need of the commutativity of the pentagonal diagram. This observation was discovered by noting the resemblance of the usual coherence theorems with certain properties of a finitely presented group known as Thompson's group F. This paper is to be taken as an advertisement for this connection.
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