Normalized Hochschild cochain complex
= Normalized Hochschild cochain complex
For a unital <associative algebra>, normalized positive-degree cochains vanish whenever an argument is $1$. They form a subcomplex of the <Hochschild cochain complex> computing the same <Hochschild cohomology>. The unit-insertion contracting homotopy on degenerate bar terms proves the normalization equivalence. A normalized degree-two <Hochschild cocycle> defines a unital <square-zero extension of an algebra>.