The notion of minimal objects generalizes the notion of minimal elements of preorders. Intuitively, minimal elements are ones that don’t have anything below them, even though they might not be the minimum. A ‘minimum object’ would be instead an initial object. Minimal objects have been first defined in (Adámek et al. ‘12) in the context of coalgebra theory, relative to an orthogonal factorization system. Trivializing the factorization system gives a general notion of minimality and maximality,..