Differential graded module
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In algebra, a differential graded module, or dg-module, is a -graded module together with a differential; i.e., a square-zero graded endomorphism of the module of degree 1 or -1, depending on the convention. In other words, it is a chain complex having a structure of a module, while a differential graded algebra is a chain complex with a structure of an algebra.
In view of the module-variant of Dold–Kan correspondence, the notion of an -graded dg-module is equivalent to that of a simplicial module; "equivalent" in the categorical sense; see #The Dold–Kan correspondence below.
The Dold–Kan correspondence
Given a commutative ring R, by definition, the category of simplicial modules are simplicial objects in the category of modules over R; denoted by sModR. There is a functor