Acyclicity Conditions on Pasting Diagrams

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-10-15 DOI:10.1007/s10485-024-09784-x

Amar Hadzihasanovic, Diana Kessler

引用次数: 0

Abstract

We study various acyclicity conditions on higher-categorical pasting diagrams in the combinatorial framework of regular directed complexes. We present an apparently weakest acyclicity condition under which the \(\omega \)-category presented by a diagram shape is freely generated in the sense of polygraphs. We then consider stronger conditions under which this \(\omega \)-category is equivalent to one obtained from an augmented directed chain complex in the sense of Steiner, or consists only of subsets of cells in the diagram. Finally, we study the stability of these conditions under the operations of pasting, suspensions, Gray products, joins and duals.

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粘贴图表的循环条件

我们在正则有向复数的组合框架中研究了高分类粘贴图的各种非循环性条件。我们提出了一个明显的最弱非循环性条件，在这个条件下，由图形状呈现的（\omega \）-类别在多图的意义上是自由生成的。然后，我们考虑了更强的条件，在这些条件下，这个（\omega \）类别等价于从斯坦纳意义上的增强有向链复合体中得到的类别，或者只由图中的单元子集组成。最后，我们研究了这些条件在粘贴、悬浮、灰积、连接和对偶等操作下的稳定性。

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.