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Concept
Differential graded module
Summary
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 sense; see below.
Given a commutative ring R, by definition, the of simplicial modules are simplicial objects in the ; denoted by sModR. Then sModR can be identified with the category of differential graded modules which vanish in negative degrees via the Dold-Kan correspondence.
Official source
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