As I understand it, in the category of sets, there is no morphism $\{1\}\rightarrow\emptyset$. On the other hand, is one permitted to say sentences like the following?
"Consider the empty family $(\phi_\alpha)_\alpha$ of morphisms, where $\phi_\alpha:\{1\}\rightarrow\emptyset$."
For example, can one say,
"Find the pullback of the empty family $(\phi_\alpha)_\alpha$ of morphisms, where $\phi_\alpha:\{1\}\rightarrow\emptyset$."