Hello,


I just need some clarification (or a good reference) for the definition of the realization of a bisimplicial set, this is what i have when $X$ is a bisimplicial set its realization is


$\cup\_n X\_n \times \Delta[n]$ subject to the following equivalence relation
$(d\_ix,p) \sim (x,d\_ip), (x,p) \in X\_n \times \Delta[n-1]$


$(s\_ix,p) \sim (x,s\_ip), (x,p) \in X\_{n-1} \times \Delta[n]$


My question is since the realization of a bisimplicial set is a simplicial set what are the k-simplicies $|X|\_k$ are? is it correct that the $|X|\_k=\cup\_n (X\_{n,k} \times \Delta[n]\_k)/\sim$ but then what is $\sim$ in this case?


Any help is appreciated. 



Realization of a bisimplicial set
I think the easiest way to see it is that :


$|X|\_k=\cup\_n (X\_{n,k} \times \Delta[n]\_k)/\sim$ subject to the following equivalence relation
$(d\_ix,p) \sim (x,d\_ip), (x,p) \in X\_{n,k} \times \Delta[n-1]\_k$


$(s\_ix,p) \sim (x,s\_ip), (x,p) \in X\_{n-1,k} \times \Delta[n]\_k$


