Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Strong version of Snake Lemma in exact categories

Pages: 151 – 163

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a9

Authors

Shi Rong (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Pu Zhang (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Abstract

We prove the strong version of Snake Lemma, and its equivalence to the other two versions of Snake Lemma, in weakly idempotent complete exact categories.

Keywords

strong version of Snake Lemma, (weakly idempotent complete) exact category, admissible morphism, morphism category, generalized abelian category, Gorenstein-projective module

2010 Mathematics Subject Classification

18C10, 18E10, 18E20, 18G50

Supported by the NNSFC (National Natural Science Foundation of China) Grant No. 11971304.

Received 7 May 2020

Received revised 14 October 2020

Accepted 23 October 2020