sandwhiched by zero object and isomorphism

1. Proposition

Let 20240119-short_exact_sequence_and_isomorphism_3038b4682e1f6d64ae501574b4029ad43f8f615e.svg be an abelian category (resp. category Group) and

20240119-short_exact_sequence_and_isomorphism_884804b41b74a0dd6a0651cd83095f25888fad38.svg

is an isomorphism
are zero morphisms

2. Proof

2.1. 1) 2)

abelian category as balanced category exact sequence and monomorphism exact sequence and epimorphisms

2.2. 2) 1)

follows as

minimal kernel and monomorphism image of an epimorphism

Date: nil

Author: Anton Zakrewski

Created: 2024-10-20 So 05:30