Sorry for the slow reply. For some reason I see this only now.

The answer is: it’s equivalent.

As indicated in the entry, this is discussed in *Principal ∞-bundles – theory, presentations and applications (schreiber)*.

I don’t have a good internet access in the near future but I wonder about the connection between the definition in the stub above and the following:

An extension of $\infty$-group is a sequence $N\to G\to Q$ of $\infty$ groups and $\infty$ group maps such that $N\to G$ is $\infty$ normal and Q is the $\infty$ qoutient

]]>quick entry for *infinity-group extension*, just so that I can complete links at related entries.