Let $\Gamma$ is a smooth projective curve, $x_1, x_2$ two distinc fixed points on $\Gamma$, and $X$ a smooth projective variety.
In definition-Lemma 1 Roitman paper "On $\Gamma$-equivalence of $0$-dimensional cycles" says:
Two cycles $A_1$ and $A_2$ in $Z_0(X)$ are $(\Gamma, x_1,x_2)$-equivalents, denoted by $A_1\sim_{\Gamma} A_2$, if there exists a one dimensional cycle $T$ on $\Gamma\times X$ such that \begin{equation*} i^*_{x_1}(T)=A_1, \text{ and } i^*_{x_2}(T)=A_2, \end{equation*} where
\begin{array}{cccc} i_{y}:& X &\rightarrow & \Gamma\times X \\ & x &\mapsto & y\times x \end{array}
Well, this definition is not clear for me yet because I think that in the above definition, $i^*_{y}$ is the pull-back of $i_y$, i.e., $i^*_{y}:Z_1(\Gamma\times X)\rightarrow Z_0(X)$, so it means that $i_y$ is flat of relative dimension $-1$ (because, as far as I know, we should need these two properties to define the pull-back). Can the relative dimension of a morphism be negative? If not, How can I justify the existence of $i^*_{y}$?