Acyclicity conditions on pasting diagrams

Amar Hadzihasanovic, Diana Kessler
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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.
粘贴图的无循环性条件
我们在规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。我们提出了一个显然是最弱的非循环性条件,在这个条件下,图形状所呈现的$\omega$类别在多图的意义上是自由生成的。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有向链增强复合体中得到的类别,或者只由图中单元的子集组成。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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