### Abstract

Let F, G:I → C be monoidal functors from a monoidal category I to a linear abelian rigid monoidal category C over an algebraically closed field k. Then the set Nat(F,G) of natural transformations F → G is naturally a vector space over k. Under certain assumptions, we show that the set of monoidal natural transformations F → G is linearly independent as a subset of Nat(F,G). As a corollary, we can show that the group of monoidal natural automorphisms on the identity functor on a finite tensor category is finite. We can also show that the set of pivotal structures on a finite tensor category is finite.

Original language | English |
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Pages (from-to) | 1939-1946 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2012 Feb 27 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics