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