Graded category
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A graded category is a mathematical concept.
If 
is a category, then a -graded category is a category 
together with a functor 
.
Monoids and groups can be thought of as 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.
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