The category is that whose objects are Lie algebras and whose morphisms are Lie algebra homomorphisms, that is linear maps such that for all we have
If Lie algebras are expressed in terms of their Chevalley–Eilenberg algebras (and if restricted to finite-dimensional Lie algebras), this may equivalently be characterized as follows:
is the full subcategory of the opposite category of the category dgAlg of dg-algebras on those dg-algebras whose underlying graded algebra is a Grassmann algebra, i.e. of the form .