I am reading some handwritten notes, and scribbled next to a restriction of scalars functor, are the words "a pullback".
I don't understand why this might be the case.
In particular, consider a field $k$ with a map $\varphi:k\rightarrow A$ for $A$ an associative unital $k$-algebra. Then we consider the induced functor $\varphi_*:A-mod\rightarrow k-mod$ restriction of scalars.
Is $\varphi_*$ the pullback of some diagram in the category of functors from $A$-mod to $k$-mod?
I know this a fairly strange question, but I just cant see what the scribbler had in mind.