proposition: Lemma has_cofiprods_functor_cat : forall a b, Category.axioms a -> has_cofiprods b -> has_cofiprods (functor_cat a b).
proof: Proof. ir. rw has_cofiprods_has_colimits_over_opp. cp H0. uh H1; ee. rwi has_cofiprods_has_colimits_over_opp H0. ap has_colimits_functor_cat. am. am. ap opp_axioms. ap vee_cat_axioms. am. am. ap functor_cat_axioms. am. uh H0; ee; am. Qed.
imports: Arith colimits little_cat fc_limits cardinal