On some sheaves over a differential space
We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.
We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.