Sheet diagrams for bimonoidal categories
Cole Comfort, Antonin Delpeuch, Jules Hedges
TL;DR
This paper introduces sheet diagrams, a graphical calculus for bimonoidal categories, providing a formal, sound, and complete representation that captures their algebraic structure through string diagrams on a branching surface.
Contribution
It formally defines sheet diagrams as a new graphical calculus for bimonoidal categories, establishing soundness and completeness results.
Findings
Sheet diagrams are sound and complete for bimonoidal categories.
They provide a visual and formal tool for reasoning about bimonoidal structures.
The calculus captures the free bimonoidal category on a given signature.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLogic, programming, and type systems · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models