This is in response to the OP's recent reference request.

It sounds like the reference you seek may be John Milnor's paper 

Construction of universal bundles. I.  Ann. of Math. (2)  63  (1956), 272–284. 

Milnor starts with the Serre path-loop fibration with fibre $\Omega X$ on a based countable simplicial complex $X$. He then replaces continuous paths (loops) with "simplicial paths (loops)". It turns out that the resulting bundle is still universal (meaning the space of based simplicial paths is contractible) and the fibre $\tilde{\Omega} X$, the space of based simplicial loops, is a topological group.