Scholarlink

<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi _2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>π</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-indexings.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Length of Fully Faithful Framed Bicategories

  • 期刊论文

  • 发表日期：

    2026年5月4日

查看全文
  • Juan Orendain

摘要

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 \(\pi _2\) π 2 -indexings.