Retracts

A "retract" of an object \(b\) in a category \(C\) is an object \(a \in Ob(C)\) such that there exists morphisms \(f : a \to b\) and \(r : b \to a\) where \(r \circ f = id_a\). The morphism \(r\) is a "retraction" of \(b\) onto \(a\).