Lie algebra representation

Source: @baez1994gauge page 197.
Recall that a group representation of $G$ on a vector space $V$ is a homomorphism $p:G\to \text{GL}(V)$. Similarly, a representation of a Lie algebra $\mathfrak{g}$ on $V$ is defined as a Lie algebra homomorphism $f:\mathfrak{g}\to \mathfrak{gl}(V)$, where $\mathfrak{gl}(V)$ denotes the Lie algebra of linear operators on $V$ under the commutator bracket. It is clear that differentiating a representation $p:G\to \text{GL}(V)$ yields a representation $dp:\mathfrak{g}\to \mathfrak{gl}(V)$ of the corresponding Lie algebra. Conversely, a deeper result asserts that if $f:\mathfrak{g}\to \mathfrak{gl}(V)$ is a representation of a simply connected Lie group $G$, it can be “exponentiated” to obtain a representation $p:G\to \text{GL}(V)$ such that $dp=f$.