In the paper integrability of Lie brackets M. Crainic and L. R. Fernandez define the notion of A-path as follows.
Definition. Let $A\stackrel{\pi}{\longrightarrow} M$ be a Lie algebroid. An A-path is a $C^1$ curve $a:I\longrightarrow A$ such that $$\sharp a(t)=\frac{d}{dt} \pi(a(t)),$$ where $\sharp:A\longrightarrow TM$ is the anchor map.
I'm trying to make sense of this definition. What does $\frac{d}{dt}\pi(a(t))$ mean? I don't understand for it should be a map from $I$ to $TM$.
Thanks.