Geometric realisations of cubical sets with connections, and classifying spaces of categories

被引：8

作者：

Antolini, R ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

APPLIED CATEGORICAL STRUCTURES | 2002年 / 10卷 / 05期

关键词：

category; classifying space; connections; cubical set; homotopy; realisation;

D O I：

10.1023/A:1020506404904

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the category of cubical sets with some additional degeneracies called connections. We prove that the realisation of a cubical set with connections is independent, up to homotopy, of whether we collapse those extra degeneracies or not and that any cubical set which is Kan admits connections. Using this type of cubical sets we define the cubical classifying space of a category and prove that this is equivalent to the simplicial one.

引用

页码：481 / 494

页数：14

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