Leroyer AS, Ebrahimian TG, Cochain
C, Recalde A, Blanc-Brude O, Mees B, et al.
In Section 2 and Section 3 we give a short overview of N-structures, such as N-differential module, cochain N-complex, generalized cohomologies of an N-complex, and graded q-differential algebra.
A cochain complex is a Z-graded differential module E = [[direct sum].
A cochain N-complex of modules or simply an N-complex is a Z-graded N-differential module E = [[direct sum].
Likewise the map U makes them into cochain complexes, i.
op] for a cochain complex C denotes the opposite chain complex that one obtains by reindexing in the opposite order and reversing all the arrows.