proposition: Lemma has_coequalizers_opp : forall a, has_coequalizers (opp a) = has_equalizers a.
proof: Proof. ir. ap iff_eq; ir. uh H; ee. uhg; ee. wrr axioms_opp. ir. rw has_eq_has_coeq. ap H0. rw twoarrow_hypothesis_opp_flip. am. wrr axioms_opp. wrr axioms_opp. uh H; ee. uhg; ee. app opp_axioms. ir. rw has_coeq_has_eq. rw opp_opp. ap H0. wr twoarrow_hypothesis_opp. am. am. app opp_axioms. Qed.
imports: Arith colimits little_cat fc_limits cardinal