5-Lemma for quasi isomorphisms

1. Proposition

Let 20240130-5_lemma_for_quasi_isomorphisms_eb04be82533afa6bcab2b0d2106fd2828974c0d1.svg be an abelian category and 20240130-5_lemma_for_quasi_isomorphisms_81ca28a09975fbedac4572d53c0b7c3d6395ae46.svg be the category of chain complexes,

20240130-5_lemma_for_quasi_isomorphisms_580a41efe70975e46e694bc76898f1a0463a0b8e.svg

a diagram of chain complexes such that

20240130-5_lemma_for_quasi_isomorphisms_15e15a70eb54aa1d0aac450a5350c409a8996024.svg

is exact wiht the respective isomorphisms

Then 20240130-5_lemma_for_quasi_isomorphisms_5461866a7289ba4c56a10a82a5622bfbdcb4ae22.svg is a quasi-isomorphism

2. Proof

corollary of Five-Lemma

Date: nil

Author: Anton Zakrewski

Created: 2024-10-14 Mo 08:49