I have a problem with question 5.7.2 (b) from Awodey's Category Theory, it says:
Let C be a category with pullbacks.
(a) Show that an arrow $m : M → X$ in C is monic if and only if the diagram below is a pullback.
Thus, as an object in C/X, m is monic iff $m × m \cong m$.
(b) Show that the pullback along an arrow $f : Y \to X$ of a pullback square over $X$,
is again a pullback over $Y$. (Hint: draw a cube and use the two-pullbacks lemma.) Conclude that the pullback functor $f^*$ preserves products.
(c) Conclude from the foregoing that in a pullback square
if $m$ is monic, then so is $m'$.
However I don't get what the question (b) is asking us - and to be honest, it is kind of confusing.
Well, he seems to suggest that we have to assume "the pullback along an arrow $f : Y → X$ of a pullback square over $X$" - but what is this supposed to mean exactly? He doesn't seem to "define" this in any part of the book.
Also, I am able to solve (c) directly. But how can we "conclude [it] from the foregoing"? How are those problems related?