Monads on Higher Monoidal Categories

被引：6

作者：

Aguiar, Marcelo ^{[1
]}

Haim, Mariana ^{[2
]}

Lopez Franco, Ignacio ^{[3
]}

机构：

[1] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

[2] Univ Republica, Fac Ciencias, Ctr Matemat, Montevideo, Uruguay

[3] Univ Republ, Dept Math & Applicat, CURE, Tacuarembo S-N, Maldonado, Uruguay

来源：

APPLIED CATEGORICAL STRUCTURES | 2018年 / 26卷 / 03期

基金：

美国国家科学基金会;

关键词：

Monoidal category; Duoidal category; Higher monoidal category; Multicategory; Monoidal monad; Comonoidal monad; Higher monoidal monad; Smash product; DUOIDAL CATEGORIES; TENSOR CATEGORIES; HOPF MONOIDS; PRODUCT;

D O I：

10.1007/s10485-017-9497-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 .

引用

页码：413 / 458

页数：46

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