关于十二指肠\(\infty \) -分类

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2025-02-13 DOI:10.1007/s40062-025-00364-x

Takeshi Torii

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引用次数: 0

摘要

二元类是一个具有两个单一型结构的类，其中一个相对于另一个是松散单一型的。本文介绍了十二指肠\(\infty \) -类，它是十二指肠类在\(\infty \) -类设置中的对应。在十二指肠\(\infty \) -范畴之间有三种函子，分别称为双轴、双lax和双双轴单函子。我们给出了三个公式\(\infty \) -十二指肠的范畴\(\infty \) -根据我们取的函子的范畴。在此基础上，针对这三种函子，分别在\(\infty \) -类中定义了双一元、双一元和双共元。

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On duoidal \(\infty \)-categories

A duoidal category is a category equipped with two monoidal structures in which one is (op)lax monoidal with respect to the other. In this paper we introduce duoidal \(\infty \)-categories which are counterparts of duoidal categories in the setting of \(\infty \)-categories. There are three kinds of functors between duoidal \(\infty \)-categories, which are called bilax, double lax, and double oplax monoidal functors. We make three formulations of \(\infty \)-categories of duoidal \(\infty \)-categories according to which functors we take. Furthermore, corresponding to the three kinds of functors, we define bimonoids, double monoids, and double comonoids in duoidal \(\infty \)-categories.

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.