Moerdijk, Classifying spaces and classifying topoi, defines the Verdier cohomology of a Grothendieck topos $\mathcal E$ by taking a limit on $HC$, the homotopy of hypercoverings in $\mathcal E$.
I have some confusion on what this homotopy category is: a hyper covering is defined as a simplicial object $X_\bullet$ in $\mathcal E$ such that $X_\bullet\to 1$ is a local trivial fibration. So what does it mean that two arrows bewteen two such hyper coverings are homotopic?
Thank you in advance.