2022/05/16 by Titouan Carette, Carette, Titouan · 1 citation
Computer Science · #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Logic, programming, and type systems #Model-Driven Software Engineering Techniques #Quantum Physics (quant-ph) #Software Engineering Research
paper · pdf · doi:10.48550/arxiv.2205.07760
openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
String diagrams can nicely express numerous computations in symmetric strict monoidal categories (SSMC). To be entirely exact, this is only true for props: the SSMCs whose monoid of objects are free. In this paper, we show a propification theorem asserting that any SSMC is monoidally equivalent to a coloured prop. As a consequence, all SSMCs are within reach of diagrammatical methods. We introduce a diagrammatical calculus of bureaucracy isomorphisms, allowing us to handle graphically non-free monoids of objects. We also connect this construction with the scalable notations previously introduced to tackle large-scale diagrammatic reasoning.