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arXiv · 2205.07760

Propification and the Scalable Comonad

Titouan Carette
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Abstract

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.

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Titouan Carette. 2022-05-16. Propification and the Scalable Comonad. https://arxiv.org/abs/2205.07760

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