definition. string diagram [nakahira2023diagrammatic, table 1.1] [tt-003V]

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A string diagram represents categories as surfaces (2-dimensional), functors as wires (1-dimensional), natural transformations as blocks or just dots (0-dimensional).

String diagrams has the advantage of being able to represent objects, arrows, functors, and natural transformations from multiple categories, and their vertical and horizontal composition, and has various topologically plausible calculational rules for proofs.