functor preserving pushouts preserves epimorphisms

1. Proposition

2. Proof

Suppose 20240109-functor_preserving_pushouts_preserves_epimorphisms_ad6a03aaa8d3a8bd22f0e7659be6109d78aaf52a.svg is an epimorphism. Then by epimorphism and pushout

20240109-functor_preserving_pushouts_preserves_epimorphisms_b663edf7e2446e781b524460a141b1e71dd717c3.svg

is a pushout.

Since 20240109-functor_preserving_pushouts_preserves_epimorphisms_f9d4fff07675f599df559c5e656b52a1fd42a7f3.svg preserves pushouts, we get

20240109-functor_preserving_pushouts_preserves_epimorphisms_b332b02f963c013c651088eb8bddf6641feac932.svg

Thus again by epimorphism and pushout, 20240109-functor_preserving_pushouts_preserves_epimorphisms_ced255899a4f5780e101ccdb15c0d1d3532e2e80.svg is an epimorphism.

Date: nil

Author: Anton Zakrewski

Created: 2024-10-19 Sa 21:31