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Constructing a morphism of free modules using the indexing set

I have a set S indexed by triplets of numbers [i,j,k], and I want to construct an endomorphism T of the free module over S (call it F(S)) of the form:

T: e[i,j,k] ---> Sum over (u,v,w) : f(i,j,k, u,v,w) e[u,v,w]

where f(ijkuvw) is a certain function.

Is there a simple way to do this?