Initial and terminal objects in $\textbf{FinVect}_R$ I am teaching myself category theory and I am having difficulties identifying the initial and terminal object of the category of $\textbf{FinVect}_R$.
I was thinking that because it is finite vectors then the initial and terminal should be the same object ( since they are finite, we can operate in those vectors until we reached that last one since it is finite).
Any help will be greatly appreciated.  

I believe the terminal and initial object are both the zero-dimensional vector space $0$. 
There is one map from $0$ to any other vector space $V$, since we must send $0$ to $0_V$. This follows from the definition of a linear map, and linear maps are the morphisms in this category. So $0$ is the initial object.
Similarly, there is exactly one morphism from any vector space $V$ to $0$: the map sending all elements to $0$. So $0$ satisfies the definition of terminal object. 
Note that this argument is independent of the base field. So you could consider the category of vector spaces over $\mathbb C$, for example, and the answer would be the same. 
