Notions of Mobius inversion

被引：9
|
作者：
Leinster, Tom [1 ]
机构：
[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland
来源：
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2012年 / 19卷 / 05期
基金：
英国工程与自然科学研究理事会;
关键词：
Mobius inversion; Mobius-Rota inversion; Euler characteristic of category; enriched category; poset; incidence algebra; unique lifting of factorizations; matrix of category; pullback-homomorphism; EULER CHARACTERISTICS; CATEGORIES; ALGEBRA;
D O I：
10.36045/bbms/1354031556
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Mobius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying abstract framework. This allows us to compare and contrast the two theories of Mobius inversion for categories, and advance each of them. Among several side benefits is an improved understanding of the following fact: the Euler characteristic of the classifying space of a (suitably finite) category depends only on its underlying graph.
引用
收藏
页码：909 / 933
页数：25
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