My understanding of natural transformations (also called canonical?) is the following:
We need two functors given, say $F_1$ and $F_2$, with $F_{1,2}:\mathbf{K}\to \mathbf{L}$, $\mathbf{K}$ and $\mathbf{L}$ categories. Then a natural transformation is an assignment $\tau : F_1 \to F_2$, which assigns to each object of $\mathbf{K}$, an $\mathbf{L}$ morphism, namely $$ \tau V: F_1(V)\to F_2(V), $$ but in such a manner that the following holds: Given any $\mathbf{K}$-morphism $f:K_1 \to K_2$, the appropriate diagram commutes: $$ F_2(f)\circ \tau K_1 = \tau K_2 \circ F_1(f). $$
Identifying an $n$-dimensional vector space $V$ with $\mathbb{R}^n$, via a choice of basis $$ L_a: \mathbb{R}^n \to V , \ \ \mathbf{x}\mapsto \sum_{i\in I}x_ia_i\in V $$ with $a_i(i\in I)$ a basis for $V$, gives me the sense that it is not canonical. Is it easy to should that it is not canonical by working with the naturality definition in the category Vect?