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.
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