Geodesic
Associativity constraints, braidings and quantizations of modules with grading and action
Lobachevskii journal of mathematics, Tome 23 (2006), pp. 5-27.

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We study quantizations, associativity constraints and braidings in the monoidal category of monoid graded modules over a commutative ring. All of them can be described in terms of the cohomology of the underlying (finite) monoid. The Fourier transform of finite groups gives a corresponding description in the monoidal category of modules with action by a group. 
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H. L. Huru. Associativity constraints, braidings and quantizations of modules with grading and action. Lobachevskii journal of mathematics, Tome 23 (2006), pp. 5-27. http://geodesic.mathdoc.fr/item/LJM_2006_23_a0/

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