Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as a class of ternary relations with both group-like and category-like properties. A hierarchy of subclasses is explored, each satisfying stronger useful algebraic properties than the preceding, culminating in a direct efficient conversion-by-rewriting algorithm.

翻译：本文基于范畴群论为带前缀的度量单位及其转换规则建立了形式化语义模型。定义了基本结构以及自然与偶发的语义运算。转换规则被表示为一类兼具群与范畴性质的三元关系。研究了一系列子类的层次结构，其中每一子类都满足比前一类更强的实用代数性质，最终导出了一个直接高效的基于重写的转换算法。