Doubly Weak Double Categories

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2026-05-04 DOI:10.1007/s10485-026-09863-1

Aaron David Fairbanks, Michael Shulman

引用次数: 0

Abstract

We propose a definition of double categories whose composition of 1-cells is weak in both directions. Namely, a doubly weak double category is a double computad—a structure with 2-cells of all possible double-categorical shapes—equipped with all possible composition operations, coherently. We also characterize them using “implicit” double categories, which are double computads having all possible compositions of 2-cells, but no compositions of 1-cells; doubly weak double categories are then obtained by a simple representability criterion. Finally, they can also be defined by adding a “tidiness” condition to the double bicategories of Verity, or to the cubical bicategories of Garner.

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双弱双范畴

我们提出了双范畴的定义，它的组成在两个方向上都是弱的。也就是说，一个双弱双范畴是一个双计算机——一个具有所有可能的双范畴形状的2个单元的结构——连贯地配备了所有可能的组合操作。我们还使用“隐式”双类别来描述它们，这是双计算，具有所有可能的2单元组成，但没有1单元组成；然后通过一个简单的可表示性准则得到双弱双范畴。最后，它们也可以通过在Verity的双类或Garner的立方类中添加一个“整齐”条件来定义。

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.