A Skew-Duoidal Eckmann-Hilton Argument and Quantum Categories

被引：0

作者：

Stephen Lack

Ross Street

机构：

[1] Macquarie University,Department of Mathematics

来源：

Applied Categorical Structures | 2014年 / 22卷

关键词：

Bialgebroid; Fusion operator; Quantum category; Monoidal bicategory; Duoidal category; Monoidale; Duoidale; Skew-monoidal category; Comonoid; Hopf monad; 18D10; 18D05; 16T15; 17B37; 20G42; 81R50;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories were originally defined as monoidal comonads on endomorphism objects in a particular monoidal bicategory ℳ. Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in ℳ. Now we see in what kind of ℳ quantum categories are merely monads.

引用

页码：789 / 803

页数：14

共 6 条

[1] A Skew-Duoidal Eckmann-Hilton Argument and Quantum Categories
Lack, Stephen
Street, Ross
APPLIED CATEGORICAL STRUCTURES, 2014, 22 (5-6) : 789 - 803
[2] The ∞-categorical Eckmann-Hilton argument
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Yanovski, Lior
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2019, 19 (06): : 3119 - 3170
[3] The Eckmann-Hilton argument and higher operads
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ADVANCES IN MATHEMATICS, 2008, 217 (01) : 334 - 385
[4] ON EXACTNESS OF ECKMANN-HILTON HOMOTOPY SEQUENCE
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CANADIAN MATHEMATICAL BULLETIN, 1966, 9 (05): : 671 - &
[5] HOMOLOGY PRODUCTS AND THE ECKMANN-HILTON GROUPS
HOWELL, K
MICHIGAN MATHEMATICAL JOURNAL, 1985, 32 (02) : 153 - 165
[6] SKEW MONOIDALES, SKEW WARPINGS AND QUANTUM CATEGORIES
Lack, Stephen
Street, Ross
THEORY AND APPLICATIONS OF CATEGORIES, 2012, 26 : 385 - 402

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