Corollary 5.57.
Let \(\Sigma\) be a small class of monomorphisms in \(T\). Then the congruence \(\Sigma^c\) generated by \(\Sigma\) is monogenic.
Proof
For a monomorphism, every positive iterated diagonal is an isomorphism. Thus \(\im(\Sigma^{\Delta})\) consists of the maps in \(\Sigma\) together with isomorphisms, which do not change the acyclic class they generate. The claim is therefore immediate from the lemma.