Thomason-Type Model Structures on Simplicial Complexes and Graphs

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2026-02-12 DOI:10.1007/s10485-026-09850-6

Emilio Minichiello

引用次数: 0

Abstract

In this paper we show that the Matsushita model structure on loop graphs, which is right-transferred from the Kan-Quillen model structure on simplicial sets, factors through two other right-transferred model structures on simplicial complexes and reflexive graphs. We show that each Quillen adjunction between these right-transferred model categories is a Quillen equivalence. These model structures are analogous to the Thomason model structure on small categories, and we prove that they are all cofibrantly generated and proper. Furthermore we show that all cofibrant simplicial complexes are flag complexes, and all forests are cofibrant.

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简单复合体和图上的thomason型模型结构

本文证明了由简单集上的Kan-Quillen模型结构右迁移而来的环图上的Matsushita模型结构，可以通过简单复合体和自反图上的另外两种右迁移模型结构进行因子化。我们证明了这些右转移模型范畴之间的每一个Quillen合都是一个Quillen等价。这些模型结构类似于小范畴上的Thomason模型结构，并证明了它们都是协生的和适当的。进一步证明了所有的共融单纯配合物都是标志配合物，所有的森林都是共融的。

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.