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Stream: learning: questions

Topic: Graphical calculus

Cole Comfort (Sep 17 2020 at 20:07):

Does anyone know if there is a sound complete graphical calculus for premonoidal categories? I am interested in this, because $( {\sf Cospan}({\sf FinSet}), \times )$ is only premonoidal and not monoidal (where $\times$ is defined pointwise). This is unlike when the tensor product is the direct sum, which admits a presentation in terms of generators and relations in a monoidal category (the prop for the free commutative frobenius algebra ).

Nathanael Arkor (Sep 17 2020 at 21:25):

Alan Jeffrey claims a sound and complete calculus for premonoidal categories in Premonoidal categories and a graphical view of programs, but the proofs are left to an appendix, which appears to be missing in that version.

Cole Comfort (Sep 17 2020 at 21:28):

Thanks!