colimit functor preserves epimorphisms

Proposition

Let C be a category, I,J:IC be diagrams, such that their colimits exist, and η:IJ a natural transformation containing only epimorphisms.
Then

colim(η)

is also an epimorphism

Proof

Date: nil

Author: Anton Zakrewski

Created: 2025-01-15 Mi 21:12