In $k$-linear triangulated categories, there is an evaluation map
$\oplus_i \text{Hom}(E,A[i])\otimes_k E[-i]\to A .$
I've learned that in the derived categorie of coherent sheafs on a scheme $X$, the tensor product $V\otimes F[-i]$ is just the direct sum of $\text{dim }V$ copies of $F[-i]$.
However, I do not understand the above construction in general triangulated $k$-linear categories. Could anyone help me to understand how the tensorproduct and the evaluation map are defined? Thank you.