{"title":"Categorical View of the Partite Lemma in Structural Ramsey Theory","authors":"Sebastian Junge","doi":"10.1007/s10485-023-09733-0","DOIUrl":null,"url":null,"abstract":"<div><p>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).</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 4","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09733-0.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Categorical Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10485-023-09733-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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).
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.
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