Dagger Categories and the Complex Numbers: Axioms for the Category of Finite-Dimensional Hilbert Spaces and Linear Contractions

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-05-26 DOI:10.1007/s10485-025-09803-5

Matthew Di Meglio, Chris Heunen

引用次数: 0

Abstract

We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and linear contractions in terms of simple category-theoretic structures and properties that do not refer to norms, continuity, or real numbers. This builds on Heunen, Kornell, and Van der Schaaf’s easier characterisation of the category of all Hilbert spaces and linear contractions.

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匕首范畴与复数：有限维希尔伯特空间范畴的公理与线性收缩

我们揭示了实数极限与范畴论极限之间的深层联系。利用实数经典表征的一种新变体，我们描述了有限维希尔伯特空间和线性收缩的范畴，这些范畴论结构和性质不涉及范数、连续性或实数。这建立在Heunen， Kornell和Van der Schaaf对所有希尔伯特空间和线性收缩的范畴的更简单的描述之上。

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.