exact sequence and epimorphisms

1. Proposition

Let 20240122-exact_sequence_and_epimorphisms_3038b4682e1f6d64ae501574b4029ad43f8f615e.svg be an additive category, 20240122-exact_sequence_and_epimorphisms_197ac571453007e6d6c6f9a83ea6b8217adad31e.svg and 20240122-exact_sequence_and_epimorphisms_6cf7094a238e76a0b8a4616a06f718e4fbdca703.svg a morphism

TFAE:

  1. 20240122-exact_sequence_and_epimorphisms_ad6a03aaa8d3a8bd22f0e7659be6109d78aaf52a.svg is an epimorphism
  2. the sequence
20240122-exact_sequence_and_epimorphisms_37c01c5b32d96c02254d83e4082bd99e793ab3ad.svg

is exact at 20240122-exact_sequence_and_epimorphisms_cc4c14df4ed502a664f3170f5946c2a8e7cd8913.svg

2. Proof

corollary of:

Date: nil

Author: Anton Zakrewski

Created: 2024-10-20 So 09:04