I am trying to read the paper Closed binomial edge ideals by Irena Peeva: https://www.degruyter.com/document/doi/10.1515/crelle-2023-0048/html
My question is related to Lemma 4.6, where it is claimed that the minimal free resolution of $S/(N_{b+1}:x_1y_b)$ is the tensor product of the Koszul complex $$\boldsymbol{K}(x_2,\dots,x_{b-1},y_{b+1},\dots,y_c)$$ with the minimal free resolution of $S/M_{b,c+1}$.
So far, the book Graded Syzygies by the same author has helped me a lot. However, I cannot find a reference for the tensor product of a Koszul complex with a free resolution. Unfortunately, I have not found anything in other books (S. Lang, Bruns/Herzog, Eisenbud) in the chapters that deal with the Koszul complex.
Can anyone help me with this? Thank you very much!