Dear all,

I'm happy to announce a solution to one of the oldest open problems in 
synthetic homotopy theory: the free higher group on a set is a set.

The proof proceeds by describing path types of pushouts as sequential 
colimits of pushouts, much like the James construction. This description 
should be useful also in many other applications. For example it gives a 
straightforward proof of Blakers-Massey.

Best wishes,
David

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