Quotient triple factorization classes

Let \(\varphi\colon T \to S\) be a morphism of logoi.

1. We call \(\varphi\) a monogenic quotient if it is a quotient map (Definition 4.19) whose kernel is a monogenic congruence.

2. We call \(\varphi\) an epigenic quotient if it is a quotient map whose kernel is an epigenic congruence.

3. We call \(\varphi\) conservative if it only inverts isomorphisms.

4. We call \(\varphi\) weakly conservative if it only inverts effective epimorphisms.