Notation 5.54.
Given a morphism \(f \colon A \to B\) in \(T\), we denote by \(A \overset{\coim(f)}{\twoheadrightarrow} \Im(f) \xhookrightarrow{\im(f)} B\) its epi-mono factorization. If \(\Sigma\) is a class of morphisms in \(T\), we define
\[\im(\Sigma) := \{\im(f) \mid f \in \Sigma\} \qquadtext{ and } \coim(\Sigma) := \{\coim(f) \mid f \in \Sigma\}.\]