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We define a general notion of centrally $\Gamma$-graded sets and groups andof their graded products, and prove some basic results about the correspondingcategories: most importantly, they form braided monoidal categories. Here,$\Gamma$ is an arbitrary (generalized) ring. The case $\Gamma$ = Z/2Z isstudied in detail: it is related to Clifford algebras and their discreteClifford groups (also called Salingaros Vee groups).

Graded sets, graded groups, and Clifford algebras