  The theory of ternary semigroups, groups and algebras is reformulated in the
abstract arrow language. Then using the reversing arrow ansatz we define
ternary comultiplication, bialgebras and Hopf algebras and investigate their
properties. The main property "to be binary derived" is considered in detail.
The co-analog of Post theorem is formulated. It is shown that there exist 3
types of ternary coassociativity, 3 types of ternary counits and 2 types of
ternary antipodes. Some examples are also presented.
