The composition of two Lie homomorphisms is again a homomorphism, and the class of all Lie groups, together with these morphisms, forms a category. Moreover, every Lie group homomorphism induces a homomorphism between the corresponding Lie algebras. Let formula_95 be a Lie group homomorphism and let formula_96 be its derivative at the identity. If we identify the Lie algebras of "G" and "H" with their tangent spaces at the identity elements then formula_96 is a map between the corresponding Lie algebras: