A co-operational bivariant theory derived from cohomology operations

A co-operational bivariant theory is a ``dual" version of Fulton–MacPherson’s operational bivaiant theory. For a given contravariant functor we define a generalized cohomology operation for continuous maps having sections, using cohomology operations. This generalized cohomology operation is related to Quillen’s Steenrod power operation. Using this generalized cohomology operation, we define \emph{a co-operational bivariant theory derived from cohomology operations}, which is a subtheory of the co-operational bivariant theory associated to the contravariant functor.