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Thank you for your answer. I think I can prove if a morphism preserves colimits then it preserves epis. but still not sure how to relate natural transformation f to fc(morphism in set). Can you explain more about that? Thanks.
Thank you for your quick reply:) I have another question, how to prove for all objects in the distributive category, every morphism C~0(intial object) is an isomorphism?
