the abelian category of sheaves of abelian groups on X, and is the sheaf of locally constant -valued functions. For a commutative Noetherian local ring R with residue field k, is the universal enveloping algebra of a graded Lie algebra π*(R) over k, known as the homotopy Lie algebra of R. (To be precise, when k has characteristic 2, π*(R) has to be viewed as an "adjusted Lie algebra".) There is a natural homomorphism of graded Lie algebras from the André–Quillen cohomology D*(k/R,k) to π*(R), which is an isomorphism if k has characteristic zero. See also global dimension bar resolution Grothendieck group Grothendieck local duality Notes References Homological algebra Binary operations