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math.CT2023★ 1 cited
Optics for Premonoidal Categories
James Hefford, Mario Román
We further the theory of optics or "circuits-with-holes" to encompass premonoidal categories: monoidal categories without the interchange law. Every premonoidal category gives rise…
math.CT2022★ 3 cited
On the Pre- and Promonoidal Structure of Spacetime
James Hefford, Aleks Kissinger
The notion of a joint system, as captured by the monoidal (a.k.a. tensor) product, is fundamental to the compositional, process-theoretic approach to physical theories. Promonoidal…