Koszul self-Ext algebra (${\mathrm{Ext}}_R^{\ast }(R/I,R/I)\cong {\Lambda }_{R/I}^{\ast }((I/I^2{)}^{\vee })$)

For an ideal generated by a finite regular sequence in a commutative ring, the self-Ext functor algebra is exterior on the degree-one dual generators. Contraction chain maps on the Koszul resolution represent those generators, square to zero, and anticommute. The exterior square-zero relations also apply in characteristic two.