Gluing pseudo functors via n-fold categories

doi:10.1007/s40062-016-0126-2

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	Gluing pseudo functors via n-fold categories
	Zheng, Weizhe
刊名	JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
	2017-03-01
卷号	12 期号:1 页码:189-271
关键词	Pseudo functor Gluing data 2-Category n-Fold category Hypercube
ISSN号	2193-8407
DOI	10.1007/s40062-016-0126-2
英文摘要	Gluing of two pseudo functors has been studied by Deligne, Ayoub, and others in the construction of extraordinary direct image functors in etale cohomology, stable homotopy, and mixed motives of schemes. In this article, we study more generally the gluing of finitely many pseudo functors. Given pseudo functors F-i : A(i) -> D defined on sub-2-categories A(i) of a 2-category C, we are concerned with the problem of finding pseudo functors C -> D extending F-i up to pseudo natural equivalences. With the help of n-fold categories, we organize gluing data for n pseudo functors into 2-categories. We establish general criteria for equivalence between such 2-categories for n pseudo functors and for n - 1 pseudo functors, which can be applied inductively to the gluing problem. Results of this article are used in Zheng (Sci China Math 58(3): 565-632, 2015) to construct extraordinary direct image functors in etale cohomology of Deligne-Mumford stacks.
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000401575900008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/25320]
专题	数学所
通讯作者	Zheng, Weizhe
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zheng, Weizhe. Gluing pseudo functors via n-fold categories[J]. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES,2017,12(1):189-271.
APA	Zheng, Weizhe.(2017).Gluing pseudo functors via n-fold categories.JOURNAL OF HOMOTOPY AND RELATED STRUCTURES,12(1),189-271.
MLA	Zheng, Weizhe."Gluing pseudo functors via n-fold categories".JOURNAL OF HOMOTOPY AND RELATED STRUCTURES 12.1(2017):189-271.