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.
Famous quotes containing the words graded and/or category:
“I don’t want to be graded on a curve.”
—Mary Carillo (b. 1957)
“The truth is, no matter how trying they become, babies two and under don’t have the ability to make moral choices, so they can’t be “bad.” That category only exists in the adult mind.”
—Anne Cassidy (20th century)