The linear-non-linear substitution 2-monad

Martin Hyland
(DPMMS, University of Cambridge)
Christine Tasson
(IRIF, Université de Paris)

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.

In David I. Spivak and Jamie Vicary: Proceedings of the 3rd Annual International Applied Category Theory Conference 2020 (ACT 2020), Cambridge, USA, 6-10th July 2020, Electronic Proceedings in Theoretical Computer Science 333, pp. 215–229.
Published: 8th February 2021.

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