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There are various different definitions of a graded category, up to the most abstract one given above. A more concrete definition of a graded abelian category is as follows:
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This article is about a concept in category theory. For the concept in cognitive psychology and philosophy, see
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is attached an element of a given monoid (resp. group), its grade. This must be compatible with
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138:{\displaystyle F\colon {\mathcal {C}}\rightarrow {\mathcal {A}}}
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282:{\displaystyle {\mathcal {S}}=\{S_{g}:g\in \mathbb {G} \}}
167:, in the sense that compositions have the product grade.
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561:{\displaystyle ({\mathcal {C}},{\mathcal {S}})}
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457:{\displaystyle g,h\in \mathbb {G} }
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518:{\displaystyle g\in \mathbb {G} }
423:{\displaystyle S_{g}S_{h}=S_{gh}}
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368:{\displaystyle {\mathcal {C}}}
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