Consider the direct image functor $f_*: Sh(X) \rightarrow Sh(Y)$, let $X$ and $Y$ be topological spaces, let $f: X \rightarrow Y$ be a continuous map, let $G \in Sh(X)$ be a sheaf. I was reading this course on sheaves:
On page 1 they define this subpresheaf $f_!G \subset f_*G$ then on page 2 in the first line they remark that:
"As $f_!$ is a subfunctor of $f_*$ it is left exact".
I wanted to ask, are subfunctors of left exact functors also left exact?