preserved pushout

1. Definition

Let 20231015-preserved_pushout_2d5d1c2bfbb1a2fca757f722875cd0787290c048.svg be categories, 20231015-preserved_pushout_570624dc5b21d1f0a192cc0f7dad2a4f870badf0.svg a functor and 20231015-preserved_pushout_cd0ff9796d5d44181802247ecadcd48ba7fe30fc.svg a pushout for the cospan

20231015-preserved_pushout_b2a12a669224d3ff11d24101420dfc0078cb4567.svg

Then 20231015-preserved_pushout_cd0ff9796d5d44181802247ecadcd48ba7fe30fc.svg is said to be preserved under 20231015-preserved_pushout_f1aeb1ac71cce52f443892bfa958e0fd4a349772.svg , if 20231015-preserved_pushout_a3864dd5a0c573b3b9bb6aec704a26182d8fc0d1.svg is also a pushout for

20231015-preserved_pushout_3f99519328c8553a351c5142830593db900c6f47.svg