通过$$\pi _2$$ -索引实现装饰二元范畴的内部化

IF 0.6 4区数学 Q3 MATHEMATICS Applied Categorical Structures Pub Date : 2024-06-22 DOI:10.1007/s10485-024-09774-z

Juan Orendain, José Rubén Maldonado-Herrera

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引用次数: 0

摘要

我们通过垂直变形范畴来处理将二元范畴提升为双范畴的问题。我们考虑了装饰二元范畴上的结构，这些结构允许我们在双范畴中正式实现沿着垂直细分滑动某些方格的论证。我们称这些结构为 $\pi _2$-索引。我们提出了一种构造，它将一个长度为1的双重内部化关联到每一个装饰2范畴上的（\pi _2\）索引。

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Internalizations of Decorated Bicategories via $$\pi _2$$ -Indexings

We treat the problem of lifting bicategories into double categories through categories of vertical morphisms. We consider structures on decorated 2-categories allowing us to formally implement arguments of sliding certain squares along vertical subdivisions in double categories. We call these structures $\pi _2$-indexings. We present a construction associating, to every $\pi _2$-indexing on a decorated 2-category, a length 1 double internalization.

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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.

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