  We construct a coherent Hopf 2-algebra as a quantization of coherent 2-group,
which consists of two Hopf coquasigroups and a coassociator. We also study
quasi coassociative Hopf coquasigroups, which are shown to be coherent Hopf
2-algebras with nontrivial coassociators. As an example, we study functions on
a Cayley algebra basis.
