Let R be a noetherian local ring with residue field k and f is a sequence of elements in R. Viewing the Koszul complex E = Kos(f) as a dg-algebra, we prove that that the map Ext*_{R/(f)}(k,k) to Ext*_{E}(k,k) is surjective. If time permits, we will discuss about the minimality of Tate's resolution of the residue field over any noetherian local ring.
