nLab gs-monoidal category (changes)

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Idea

A gs-monoidal category is a symmetric monoidal category that supplies cocommutative comonoid objects.

Related concepts

For now, see §6.6 of Corradini and & Gadducci 1999.

References

The notion originates in under the following, name motivated byS-monoidal categories, motivated by term rewriting , under in: the nameS-monoidal category:

• Fabio Gadducci, On the algebraic approach to concurrent term rewriting, PhD thesis (1996) [[pdf](https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=1277313dd2c4fce640780b7472221156579e392f), pdf]

after which it was renamed to gs-monoidal category in:gs-monoidal categories, in:

• Andrea Corradini, Fabio Gadducci, An algebraic presentation of term graphs, via gs-monoidal categories, Applied Categorical Structures 7 (1999) 299-331 [[doi:10.1023/A:1008647417502](https://doi.org/10.1023/A:1008647417502)]

Discussion in category theoretic probability theory:

• Tobias Fritz, Wendong Liang, Free gs-monoidal categories and free Markov categories, Appl. Categ. Structures 31 21 (2023) [[arXiv:2204.02284](https://arxiv.org/abs/2204.02284), doi:10.1007/s10485-023-09717-0]

gs-monoidal The categories notion were was reintroduced as under the nameCD-categories (for copy and discard) in:

• Kenta Cho Cho, andBart Jacobs, Disintegration and Bayesian inversion via string diagrams , Mathematical Structures in Computer Science 29.7 (2019): 938-971.29 7 (2019) 938-971 [[arXiv:1709.00322](https://arxiv.org/abs/1709.00322), doi:10.1017/S0960129518000488]