I am studying a definition of an extensive category:
An extensive category is a category $E$ with finite coproducts such that pullbacks of finite-coproduct injections along arbitrary morphisms exist and finite coproducts are disjoint and stable under pullback.
I would like to verify my understanding of the part "pullbacks of finite-coproduct injections along arbitrary morphisms exist": Let $f_A:A \to C$ and $f_B:B \to C$ be arbitrary morphisms.
Does that part imply that there exists a pullback $P$ with some morphisms $p_A:P \to A$ and $p_B:P \to B$ such that $f_A \circ p_A = f_B \circ p_B$?
Are these morphisms $p_A$ and $p_B$ (called) finite-coproduct injections? But then how does their finite-coproduct relate to the pullback $P$?
To be honest, I think I am lost. If I could see the words transformed to the symbols, it would remove ambiguity and uncertainty for me.