right exact functor and exact sequence

1. Proposition

Let 20240122-covariant_right_exact_functor_and_exact_sequence_8d761a8e0310248d2b232dd1cfa3d15c4ce348ba.svg be abelian categories and 20240122-covariant_right_exact_functor_and_exact_sequence_4834e0933441585e455612f47acbea83f96321b7.svg be an enriched functor. TFAE:

  1. 20240122-covariant_right_exact_functor_and_exact_sequence_f9d4fff07675f599df559c5e656b52a1fd42a7f3.svg is an corightexactfunctor covariant right exact functor
  2. for an exact sequence 20240122-covariant_right_exact_functor_and_exact_sequence_a469e984f4d9288fc52af58391786ee277d5b908.svg, the induced sequence
20240122-covariant_right_exact_functor_and_exact_sequence_1eba808219d85f9acad3a46121d199e9d1c5a678.svg

is also exact

2. Proof

follows dually from right exact functor and exact sequence

Date: nil

Author: Anton Zakrewski

Created: 2024-10-20 So 09:02