Categorical View of the Partite Lemma in Structural Ramsey Theory

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2023-08-04 DOI:10.1007/s10485-023-09733-0

Sebastian Junge

引用次数: 1

Abstract

We construct the main object of the Partite Lemma as the colimit over a certain diagram. This gives a purely category theoretic take on the Partite Lemma and establishes the canonicity of the object. Additionally, the categorical point of view allows us to unify the direct Partite Lemma in Nešetřil and Rödl (J Comb Theory Ser A 22(3):289–312, 1977; J Comb Theory Ser A 34(2):183–201, 1983; Discrete Math 75(1–3):327–334, 1989) with the dual Paritite Lemma in Solecki (J Comb Theory Ser A 117(6):704–714, 2010).

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结构拉姆齐理论中部引理的范畴观

我们将部引理的主要对象构造为某图上的极限。这给了部引理一个纯范畴论的看法，并建立了对象的规定性。此外，直言观点允许我们统一Nešetřil和Rödl中的直接部引理(J Comb Theory Ser 22(3): 289-312, 1977;[J] .地球物理学报，34(2):393 - 398;离散数学75(1-3):327-334,1989)与双粒子引理(Solecki) [J] .数学学报，17(6):744 - 744,2010)。

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.