exact sequence and monomorphism

1. Proposition

Let 20240122-exact_sequence_and_monomorphism_3038b4682e1f6d64ae501574b4029ad43f8f615e.svg be an additive category, 20240122-exact_sequence_and_monomorphism_197ac571453007e6d6c6f9a83ea6b8217adad31e.svg and 20240122-exact_sequence_and_monomorphism_6cf7094a238e76a0b8a4616a06f718e4fbdca703.svg a morphism

TFAE:

  1. 20240122-exact_sequence_and_monomorphism_ad6a03aaa8d3a8bd22f0e7659be6109d78aaf52a.svg is a monomorphism
  2. the sequence
20240122-exact_sequence_and_monomorphism_a6e93028004a1b7096bad8e47565f31706b9e354.svg

is exact at 20240122-exact_sequence_and_monomorphism_916c362ec11687631f4cc94f340c13fef3d5f949.svg for arbitrary 20240122-exact_sequence_and_monomorphism_e91fa320a5107d28ca27dd32ae304a1aabed4a12.svg module

2. Proof

corollary of:

Date: nil

Author: Anton Zakrewski

Created: 2024-10-20 So 09:05