proposition: Lemma equalizer_cone_equalizer : forall a u v, has_equalizer a u v -> equalizer_cone a u v (equalizer a u v) = limit (twoarrow_functor a u v).
proof: Proof. ir. uf equalizer. wr equalizer_cone_eq. tv. uh H; ee; am. ap is_limit_is_cone. ap is_limit_limit. uh H; ee; am. rw socle_limit. tv. uh H; ee; am. Qed.
imports: Arith colimits little_cat fc_limits cardinal