Homotopy colimits of 2-functors

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2016-10-31 DOI:10.1007/s40062-016-0150-2

A. M. Cegarra, B. A. Heredia

引用次数: 0

Abstract

Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend lower categorical analogues that have been classically used in algebraic topology and algebraic K-theory, such as the homotopy invariance theorem (by Bousfield and Kan), the homotopy colimit theorem (Thomason), Theorems A and B (Quillen), or the homotopy cofinality theorem (Hirschhorn).

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2函子的同伦极限

像范畴一样，小的2范畴也有很好理解的分类空间。本文讨论了用两范畴的二图表示的同伦类型。我们的结果推广了代数拓扑和代数k理论中经典使用的下范畴类似物，如同伦不变量定理(由Bousfield和Kan提出)，同伦极限定理(由Thomason提出)，定理A和定理B(由Quillen提出)，或同伦共通性定理(由Hirschhorn提出)。

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

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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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.