The Leibniz PROP is a Crossed Presimplicial Algebra

IF 0.5 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-07-30 DOI:10.1007/s10485-025-09820-4

Murat Can Aşkaroğulları, Atabey Kaygun

引用次数: 0

Abstract

We prove that the Leibniz PROP is isomorphic as \(\Bbbk \)-linear categories (not as monoidal categories) to the symmetric crossed presimplicial algebra \(\Bbbk [(\Delta ^+)^{op} \mathbb {S}]\) where \(\Delta ^+\) is the skeletal category of finite well-ordered sets with surjections, but the distributive law between \((\Delta ^+)^{op}\) and the symmetric groups \(\mathbb {S} = \bigsqcup _{n\ge 1} S_n\) is not the standard one.

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莱布尼茨PROP是一个交叉预简单代数

证明了Leibniz PROP与对称交叉预简单代数\(\Bbbk [(\Delta ^+)^{op} \mathbb {S}]\)同构为\(\Bbbk \) -线性范畴（而不是一元范畴），其中\(\Delta ^+\)是带抛射的有限良序集合的骨架范畴，但\((\Delta ^+)^{op}\)与对称群\(\mathbb {S} = \bigsqcup _{n\ge 1} S_n\)之间的分配律不是标准分配律。

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.