一句话：提出幺半宽度，作为幺半范畴中态射的复杂度度量，通过幺半分解惩罚大对象复合，统一刻画树宽、秩宽与矩阵秩。
论文引入“幺半宽度”作为幺半范畴中态射复杂度的度量。受图的结构宽度（如树宽、秩宽）启发，该度量基于语法分解：态射的幺半分解是使用幺半积与复合运算书写该态射的表达式；它惩罚沿“大”对象的复合，同时鼓励使用幺半积。作者证明，通过为图选择适当的范畴代数进行分解，可以分别刻画树宽与秩宽；对于矩阵，幺半宽度与秩相关。这些结果表明，幺半宽度可作为以幺半范畴态射建模的过程的结构复杂度度量。
We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition: a monoidal decomposition of a morphism is an expression in the language of monoidal categories, where operations are monoidal products and compositions, that specifies this morphism. Monoidal width penalises the composition operation along ``big'' objects, while it encourages the use of monoidal products. We show that, by choosing the correct categorical algebra for decomposing graphs, we can capture tree width and rank width. For matrices, monoidal width is related to the rank. These examples suggest monoidal width as a good measure for structural complexity of processes modelled as morphisms in monoidal categories.