Definition 2.8.29.1.2.  Let R be a ring. We define:
LMod(R) :=: {[M, , 0, , ]R | M is a set, :M × M → M is an operation on M, 0 ∈ M, :M → M is a function, : (R) × M → M is an operation such that (M, , 0, , ) forms a left R-module}
[M, , 0, , ]R = [N, , 0, , ]R  :⇔  ∃ φ:M ↔ N : [φ and 0φ0 and φ and φ]  (M is a set, :M × M → M is an operation on M, 0 ∈ M, :M → M is a function, : (R) × M → M is an operation, N is a set, :N × N → N is an operation on N, 0 ∈ N, :N → N is a function, : (R) × N → N is an operation with suitable conditions)
We write “let M be a left R-module” for “let M ∈ LMod(R).”
References.