  We introduce the concept of Hom-associative algebra structures in
Loday-Pirashvili category.The cohomology theory of Hom-associative algebras in
this category is studied.Some applications on deformation and abelian extension
theory are given. We also introduce the notion of Nijenhuis operators to
describe trivial deformations. It is proved that equivalent classes of abelian
extensions are one-to-one correspondence to the elements of the second
cohomology groups.
