A Model of Directed Graph Cofiber

被引：1

作者：

McGuirk, Zachary ^{[1
]}

Park, Byungdo ^{[2
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, IL-91904 Jerusalem, Israel

[2] Chungbuk Natl Univ, Dept Math Educ, Cheongju 28644, South Korea

来源：

AXIOMS | 2022年 / 11卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

directed graphs; graph homotopy; cofiber; category theory; path-space homology; combinatorics; PATH HOMOLOGY THEORY; DIGRAPHS; COHOMOLOGY; HOMOTOPY;

D O I：

10.3390/axioms11010032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give a construction of a cofiber of a directed graph map whose image is contractible in the cofiber. Our work reveals that a category-theoretically correct construction in continuous setup is no longer correct when it is discretized and hence leads to look at canonical constructions in category theory in a different perspective.

引用

页数：6

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