Monoidal Context Theory
<|reference_start|>Monoidal Context Theory: We universally characterize the produoidal category of monoidal lenses over a monoidal category. In the same way that each category induces a cofree promonoidal category of spliced arrows, each monoidal category induces a cofree produoidal category of monoidal spliced arrows; monoidal lenses are the free normalization of the cofree produoidal category of monoidal spliced arrows. We apply the characterization of symmetric monoidal lenses to the analysis of multi-party message-passing protocols. We introduce a minimalistic axiomatization of message passing -- message theories -- and we construct combinatorially the free message theory over a set. Symmetric monoidal lenses are the derivations of the free message theory over a symmetric monoidal category.<|reference_end|>
@article{román2024monoidal,
    title={Monoidal Context Theory},
    author={Mario Rom'an},
    journal={arXiv preprint arXiv:2404.06192},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.06192},
    primaryClass={math.CT cs.LO}
}