关于粉碎积和正则关联性的说明

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-10-19 DOI:10.1007/s10485-024-09787-8

Marco Grandis

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引用次数: 0

摘要

我们希望以有机的方式全面研究尖拓扑空间的粉碎积，而不依赖于某些 "方便的子类"。n-ary 砸积具有 "colax "形式的关联性，它为这一运算的性质及其与函数空间的联系提供了一个分类框架。书中给出了粉碎积的各种具体计算，包括关联性失效的一大类情况。在范畴理论中，Lax 和 colax 单环结构是不寻常而有趣的。本注释的某些部分对拓扑学家来说是显而易见的，而另一些部分则对分类学家来说是显而易见的，以便兼顾这两种背景。

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A Note on the Smash Product and Regular Associativity

We want to study the smash product of pointed topological spaces, in an organic way and full generality, without relying on some ‘convenient subcategory’. The n-ary smash product has a ‘colax’ form of associativity, which supplies a categorical framework for the properties of this operation and its connection with the function spaces. Various concrete computations of smash products are given, including a large class of cases where associativity fails. Lax and colax monoidal structures are unusual and interesting, in category theory. Some parts of this note will be obvious to a topologist and others to a categorist, in order to take into account both backgrounds.

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.