A Pullback Diagram in the Coarse Category

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2022-12-27 DOI:10.1007/s10485-022-09707-8

Elisa Hartmann

引用次数: 3

Abstract

This paper studies the asymptotic product of two metric spaces. It is well defined if one of the spaces is visual or if both spaces are geodesic. In this case the asymptotic product is the pullback of a limit diagram in the coarse category. Using this product construction we can define a homotopy theory on coarse metric spaces in a natural way. We prove that all finite colimits exist in the coarse category.

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粗类的回调图

本文研究了两个度量空间的渐近积。如果其中一个空间是可视的，或者两个空间都是测地线，则定义良好。在这种情况下，渐近积是一个粗糙范畴的极限图的回拉。利用这个积构造，我们可以很自然地定义粗糙度量空间上的同伦理论。证明了所有有限极限在粗范畴中都存在。

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.