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arXiv · 2010.13361

Sheet diagrams for bimonoidal categories

Cole Comfort·Antonin Delpeuch·Jules Hedges
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Abstract

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.

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Cole Comfort, Antonin Delpeuch, Jules Hedges. 2020-10-26. Sheet diagrams for bimonoidal categories. https://arxiv.org/abs/2010.13361

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