The identity homomorphism of a group G is the homomorphism ι ι G : G → → G that maps each element of G to itself. An inverse homomorphism of a homomorphism φ φ : G → → H is a homomorphism ψ ψ : H → → G such that ψ ψ ∘ ∘ φ φ = ι ι G and ⁠ φ φ ∘ ∘ ψ ψ = ι ι H ⁠, that is, such that ψ ψ ( φ φ ( g ) ) = g for all g in G and such that φ φ ( ψ ψ ( h ) ) = h for all h in ⁠ H ⁠. An isomorphism is a homomorphism that has an inverse homomorphism; equivalently, it is a bijective homomorphism. Groups G and H are called isomorphic if there exists an isomorphism ⁠ φ φ : G → → H ⁠. In this case, H can be obtained from G simply by renaming its elements according to the function ⁠ φ φ ⁠ ; then any statement true for G is true for ⁠ H ⁠, provided that any specific elements mentioned in the statement are also renamed.