We show that the category of optics in a monoidal category arises naturally from the free cornering of that category. Further, we show that the free cornering of a monoidal category is a natural setting in which to work with comb diagrams over that category. The free cornering admits an intuitive graphical calculus, which in light of our work may be used to reason about optics and comb diagrams.
翻译:我们显示,单向类别中的光学类别自然产生于该类别的自由角落。 此外,我们显示,单向类别中的自由角落是一个自然环境,可以在该类别上使用梳子图。 自由角落中包含了直观的图形计算,根据我们的工作可以用来解释光学和梳子图。