Hom weak ω-categories of a weak ω-category

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2022-04-01 DOI:10.1017/S0960129522000111
Thomas Cottrell, Soichiro Fujii
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引用次数: 1

Abstract

Abstract Classical definitions of weak higher-dimensional categories are given inductively, for example, a bicategory has a set of objects and hom categories, and a tricategory has a set of objects and hom bicategories. However, more recent definitions of weak n-categories for all natural numbers n, or of weak $\omega$ -categories, take more sophisticated approaches, and the nature of the ‘hom is often not immediate from the definitions’. In this paper, we focus on Leinster’s definition of weak $\omega$ -category based on an earlier definition by Batanin and construct, for each weak $\omega$ -category $\mathcal{A}$ , an underlying (weak $\omega$ -category)-enriched graph consisting of the same objects and for each pair of objects x and y, a hom weak $\omega$ -category $\mathcal{A}(x,y)$ . We also show that our construction is functorial with respect to weak $\omega$ -functors introduced by Garner.
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弱ω-类别的弱ω-类别
摘要归纳地给出了弱高维范畴的经典定义,如双范畴有一组对象和若干范畴,三范畴有一组对象和若干范畴。然而,最近对所有自然数n的弱n-类别的定义,或弱$ $ -类别的定义,采用了更复杂的方法,并且“家”的性质通常不是直接从定义中得到的。本文在Batanin先前的定义基础上,重点讨论了Leinster对弱$\omega$ -范畴的定义,并构造了对于每一个弱$\omega$ -范畴$\mathcal{A}$,一个由相同对象组成的底层(弱$\omega$ -范畴)富图,对于每一对对象x和y,一个弱$\omega$ -范畴$\mathcal{A}(x,y)$。我们也证明了我们的构造对于加纳引入的弱函子是泛函的。
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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