Length of Fully Faithful Framed Bicategories

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2026-05-04 DOI:10.1007/s10485-026-09861-3

Juan Orendain

引用次数: 0

Abstract

The length of a double category is a numerical invariant that quantifies the amount of ”work” required to rebuild the double category from its purely globular data. The minimal possible length is 1. It is conjectured that every framed bicategory realizes this minimal value. In this paper we confirm the conjecture for a subclass of framed bicategories: those whose unit squares are all cartesian/op-cartesian. We refer to such structures as fully-faithful/absolutely dense framed bicategories. The conjecture follows from a result relating the internal structure of fully faithful/absolutely dense framed bicategories to crossed products of decorated bicategories by \(\pi _2\)-indexings.

查看原文本刊更多论文

完全忠实框架双范畴的长度

双类别的长度是一个数值不变量，它量化了从纯全局数据重建双类别所需的“工作量”。最小可能的长度是1。据推测，每一个框架分类都实现了这个最小值。在本文中，我们证实了一类框架双范畴的一个子类的猜想：它们的单位平方都是笛卡尔/算子笛卡尔的。我们把这样的结构称为完全忠实/绝对密集的框架双范畴。通过\(\pi _2\) -索引将完全忠实/绝对密集框架双类别的内部结构与修饰双类别的交叉积联系起来，从而得出了该猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.