Googling for "atomic morphism" gives me only 70 results. Is this concept so fruitless or does it have another standard name? What I mean is a morphism $f: A \rightarrow B$ such that $(\forall g,h)\ f = g \circ h \rightarrow (g = f\ \wedge\ h = id_A)\ \vee\ (g = id_B\ \wedge\ h = f)$.

Googling for "atomic morphism" gives me only 70 results. Is this concept so fruitless or does it have another standard name? What I mean is a morphism $f: A \rightarrow B$ such that

$$(\forall g,h)\ f = g \circ h \rightarrow (g = f\ \wedge\ h = id_A)\ \vee\ (g = id_B\ \wedge\ h = f).$$

Googling for "atomic morphism" gives me only 70 results. Is this concept so fruitless or does it have another standard name? What I mean is a morphism $f$ such that $f = g \circ h \rightarrow (g = f\ \wedge\ h = id)\ \vee\ (g = id\ \wedge\ h = f)$.

Googling for "atomic morphism" gives me only 70 results. Is this concept so fruitless or does it have another standard name? What I mean is a morphism $f: A \rightarrow B$ such that $(\forall g,h)\ f = g \circ h \rightarrow (g = f\ \wedge\ h = id_A)\ \vee\ (g = id_B\ \wedge\ h = f)$.