I am reading about the contra-variant Yoneda functor and I am bit confused about what objects actually are in the Hom set.
More specifically, if $Hom(-,x):\mathcal{C}^{op}\rightarrow Set$ is the contra-variant Yoneda functor, then are the elements of $Hom(-,x)(y) = Hom(y,x)$ morphisms in $\mathcal{C}$ between $y$ and $x$? Or are they morphisms in $\mathcal{C}^{op}$ from $y$ to $x$, which then would correspond to morphism $x$ to $y$ in $\mathcal{C}$?