  This paper introduces a categorification of $k$-algebras called 2 -algebras,
where k is a commutative ring. We define the 2-algebras as a 2-category with
single object in which collections of all 1-morphisms and all 2-morphisms are
k-algebras. It is shown that the category of 2 -algebras is equivalent to the
category of crossed modules in commutative k -algebras. Also we define the
notion of homotopy for 2-algebras and we explore the relations of crossed
module homotopy and 2-algebra homotopy.
