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