论文标题
双子体类别的纸图
Sheet diagrams for bimonoidal categories
论文作者
论文摘要
双子体类别（也称为钻机类别）是具有两个单素结构的类别，其中一种分布在另一个。我们正式定义了表图，这是Staton非正式介绍的双子体类别的图形演算。纸图是在分支表面上绘制的弦图，该图本身就是挤出的弦图。我们的主要结果是图形骨化的通常形式的合理性和完整定理：我们在签名上表明，表图构成了自由的双子体类别。
Bimonoidal categories (also known as rig categories) are categories with two monoidal structures, one of which distributes over the other. We formally define sheet diagrams, a graphical calculus for bimonoidal categories that was informally introduced by Staton. Sheet diagrams are string diagrams drawn on a branching surface, which is itself an extruded string diagram. Our main result is a soundness and completeness theorem of the usual form for graphical calculi: we show that sheet diagrams form the free bimonoidal category on a signature.
