On the linear independency of monoidal natural transformations

Details On the linear independency of monoidal natural transformations On the linear independency of monoidal natural transformations

2010-08-10

arxiv.org/abs/1008.1692v2

Mathematics

Category Theory

7 pages; Some corrections in Section 3

Scientific paper

Let $F, G: \mathcal{I} \to \mathcal{C}$ be strong monoidal functors from a skeletally small monoidal category $\mathcal{I}$ to a tensor category $\mathcal{C}$ over an algebraically closed field $k$. The set $Nat(F, G)$ of natural transformations $F \to G$ is naturally a vector space over $k$. We show that the set $Nat_\otimes(F, G)$ of monoidal natural transformations $F \to G$ 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.

Affiliated with

Also associated with

No associations

Rating

On the linear independency of monoidal natural transformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the linear independency of monoidal natural transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the linear independency of monoidal natural transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-583661