  A heap is a structure with a ternary operation which is intuitively a group
with forgotten unit element. Quantum heaps are associative algebras with a
ternary cooperation which are to the Hopf algebras what heaps are to groups,
and, in particular, the category of copointed quantum heaps is isomorphic to
the category of Hopf algebras. There is an intermediate structure of a cop in
monoidal category which is in the case of vector spaces to a quantum heap about
what is a coalgebra to a Hopf algebra. The representations of Hopf algebras
make a rigid monoidal category. Similarly the representations of quantum heaps
make a kind of category with ternary products, which we call a heapy category.
