极限与2极限的比较

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2023-10-04 DOI:10.1007/s40062-023-00331-4

Ilia Pirashvili

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引用次数: 0

摘要

2-极限(也称为伪极限)是极限的2类类比，因此是一个非常重要的构造。然而，计算它比计算极限要复杂得多。本文的目的是给出这两个结构重合的条件。虽然我们的结果适用的环境是非常具体的，但它实际上是相当重要的:正如前面的文章所示，基本群可以使用2- collimit来计算。本文的结果与从有限覆盖上计算基群的情况完全一致。我们还在最后一节优化了我们的条件，从指数复杂度降低到多项式复杂度。

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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Comparison of the colimit and the 2-colimit

The 2-colimit (also referred to as a pseudo colimit) is the 2-categorical analogue of the colimit and as such, a very important construction. Calculating it is, however, more involved than calculating the colimit. The aim of this paper is to give a condition under which these two constructions coincide. Tough the setting under which our results are applicable is very specific, it is, in fact, fairly important: As shown in a previous paper, the fundamental groupoid can be calculated using the 2-colimit. The results of this paper corresponds precisely to the situation of calculating the fundamental groupoid from a finite covering. We also optimise our condition in the last section, reducing from exponential complexity to a polynomial one.

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.