On the linear independency of monoidal natural transformations

研究成果: Article

抜粋

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.

元の言語English
ページ(範囲)1939-1946
ページ数8
ジャーナルProceedings of the American Mathematical Society
140
発行部数6
DOI
出版物ステータスPublished - 2012 2 27
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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