proposition: Lemma ump_quotient_algebra : {f : Homomorphism A B | ∀ s (x y : A s), Φ s x y → f s x = f s y} <~> Homomorphism (A/Φ) B.
proof: Proof. apply (equiv_adjointify ump_quotient_algebra_lr ump_quotient_algebra_rl). - intro G. apply path_hset_homomorphism. funext s. exact (eissect (equiv_quotient_ump (Φ s) _) (G s)). - intro F. apply path_sigma_hprop. by apply path_hset_homomorphism. Defined.
imports: HoTT.Classes.interfaces.ua_congruence HSet Colimits.Quotient Classes.implementations.list Classes.interfaces.canonical_names Classes.theory.ua_homomorphism