• Corpus ID: 238582820

Free Commutative Monoids in Homotopy Type Theory

@article{Choudhury2021FreeCM,
  title={Free Commutative Monoids in Homotopy Type Theory},
  author={Vikraman Choudhury and Marcelo P. Fiore},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.05412}
}
We develop a constructive theory of finite multisets, defining them as free commutative monoids in Homotopy Type Theory. We formalise two algebraic presentations of this construction using 1-HITs, establishing the categorical universal property for each and thereby their equivalence. These presentations correspond to equational theories including a commutation axiom. In this setting, we prove important structural combinatorial properties of singleton multisets arising from concatenations and… 
1 Citations
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