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arXiv · 1701.03028

Monads on higher monoidal categories

Marcelo Aguiar·Mariana Haim·Ignacio Lopez Franco
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Abstract

We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad. Monoidal monads and comonoidal monads appear as the base cases in this hierarchy. Monads acting on duoidal categories constitute the next case. We cover the general case of $n$-monoidal categories and discuss several naturally occurring examples in which $n\leq 3$.

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Marcelo Aguiar, Mariana Haim, Ignacio Lopez Franco. 2017-01-11. Monads on higher monoidal categories. https://arxiv.org/abs/1701.03028

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