Chain Complexes

This chapter has two goals. Firstly, we summarise the sign conventions that we use in the subsequent chapter about algebraic surgery and in fact throughout the book. We use those that are standard in textbooks on algebraic topology. Section IV.9 of the textbook [134] in particular contains what is the standard definition of hom of chain complexes as a chain complex and also the tensor product of chain complexes as a chain complex. These conventions follow the Koszul sign convention [134, Remark 9.8], which is also standard.