Graded category

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A graded category is a mathematical concept.

If \mathcal{A} is a category, then a \mathcal{A}-graded category is a category \mathcal{C} together with a functor F:\mathcal{C} \rightarrow \mathcal{A}.

Monoids and groups can be thought of categories with a single element. A monoid-graded or group-graded category is therefore one in which to each morphism is attached an element of a given monoid (resp. group), its grade. This must be compatible with composition, in the sense that compositions have the product grade.

See also 
graded algebra.
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