3 x 3 lemma and protomodularity

被引：75

作者：

Bourn, D ^{[1
]}

机构：

[1] Univ Littoral, F-59379 Dunkerque, France

来源：

JOURNAL OF ALGEBRA | 2001年 / 236卷 / 02期

关键词：

short exact sequence; short five lemma; 3; x; lemma; abelian category; regular and protomodular category;

D O I：

10.1006/jabr.2000.8526

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The classical 3 x 3 lemma and snake lemma, valid in any abelian category, still hold in any quasi-pointed (the map 0 --> 1 is a mono), regular, and protomodular category. Some applications are given, in this abstract context, concerning the denormalization of kernel maps and the normalization of internals groupoids (i.e., associated crossed modules). (C) 2001 Academic Press.

引用

页码：778 / 795

页数：18

共 13 条

[1]

Barr M., 1971, Exact Categories and Categories of Sheaves, P1

[2] Normal subobjects and Abelian objects in protomodular categories [J].

Bourn, D .

JOURNAL OF ALGEBRA, 2000, 228 (01) :143-164

[3]

BOURN D, 1991, LECT NOTES MATH, V1488, P43

[4] POLYHEDRAL MONADICITY OF N-GROUPOIDS AND STANDARDIZED ADJUNCTION [J].

BOURN, D .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1995, 99 (02) :135-181

[5]

Bourn D., 2000, Theory and Applications of Categories, V7, P206

[6]

Brown R., 1976, CAH TOP GEOM DIFF, V17, P343

[7] HOMOTOPICAL ASPECTS OF LIE-ALGEBRAS [J].

ELLIS, GJ .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1993, 54 :393-419

[8]

GRAN M, 1999, THESIS LOUVAIN NEUVE

[9]

JANELIDZE G, 1999, SEMIABELIAN CATEGORI

[10] CROSSED-MODULES AND HOMOLOGY [J].

LADRA, M ;

GRANDJEAN, AR .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1994, 95 (01) :41-55

← 1 2 →