Remark [efr-001R]

A weak Segal category is similar to a virtual double category: we don't directly have a composition operator \mathbb {C}_1 \times _{\mathbb {C}_0} \mathbb {C}_1---rather, we have a category of "compositions" \mathbb {C}_2, each of which contains three faces in \mathbb {C}_1. Hence we have a choice of composites for every composable pair, although it is uniquely defined up to contractible choice.