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This document introduces the jellyfish partition category J P(n), a monoidal category that generalizes partition diagrams and is shown to be equivalent to the representation category of the alternating group An under certain conditions. The paper presents two main theorems: the first establishes that a functor from J P(n) to Rep(An) is full, while the second confirms its faithfulness under specific field characteristics. Additionally, the document discusses the relationship between jellyfish categories and

Author

evrendurdu

Language

EN