English

The linear-non-linear substitution 2-monad

Category Theory 2021-02-09 v2 Logic in Computer Science

Abstract

We introduce a general construction on 2-monads. We develop background on maps of 2-monads, their left semi-algebras, and colimits in 2-category. Then, we introduce the construction of a colimit induced by a map of 2-monads, show that we obtain the structure of a 2-monad and give a characterisation of its algebras. Finally, we apply the construction to the map of 2-monads between free symmetric monoidal and the free cartesian 2-monads and combine them into a linear-non-linear 2-monad.

Keywords

Cite

@article{arxiv.2005.09559,
  title  = {The linear-non-linear substitution 2-monad},
  author = {Martin Hyland and Christine Tasson},
  journal= {arXiv preprint arXiv:2005.09559},
  year   = {2021}
}

Comments

In Proceedings ACT 2020, arXiv:2101.07888

R2 v1 2026-06-23T15:39:54.949Z