Universal Finite Functorial Semi-norms

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-07-19 DOI:10.1007/s10485-024-09777-w

Clara Löh, Johannes Witzig

引用次数: 0

Abstract

Functorial semi-norms on singular homology measure the “size” of homology classes. A geometrically meaningful example is the \(\ell ^1\)-semi-norm. However, the \(\ell ^1\)-semi-norm is not universal in the sense that it does not vanish on as few classes as possible. We show that universal finite functorial semi-norms do exist on singular homology on the category of topological spaces that are homotopy equivalent to finite CW-complexes. Our arguments also apply to more general settings of functorial semi-norms.

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通用有限函数半规范

奇异同调的函数半规范衡量同调类的 "大小"。一个有几何意义的例子是 \(\ell ^1\)-半规范。然而，(\ell ^1\)-半规范并不普遍，因为它不会在尽可能少的类上消失。我们证明，在同构等价于有限 CW 复数的拓扑空间类别上，奇异同调上确实存在通用的有限函式半规范。我们的论证也适用于更一般的函数半规范。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.