On the linear independency of monoidal natural transformations

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1939-1946
Number of pages8
JournalProceedings of the American Mathematical Society
Volume140
Issue number6
DOIs
Publication statusPublished - 2012
Externally publishedYes

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Tensors
Vector spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the linear independency of monoidal natural transformations. / Shimizu, Kenichi.

In: Proceedings of the American Mathematical Society, Vol. 140, No. 6, 2012, p. 1939-1946.

Research output: Contribution to journalArticle

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