$d(x \otimes y) = dx \otimes y + (-1)^k x \otimes y$dy$if x has degree k. It matters. 1 There was a case where a paper proved a very strong result and the referee found an unfixable hole in the proof caused by forgetting the sign in the Puppe sequence! As others have said, it is analogous to the sign in the tensor product of chain complexes:$d(x \otimes y) = dx \otimes y + (-1)^k x \otimes y\$