Notation to indicate a function is an aggregate of a family of sub-functions?

I have a bunch of component cost functions $$C_g(x)$$ and an aggregate cost function which is defined as a weighted sum of components $$\sum_{g=1}^G \omega_g C_g(x)$$. Currently I write $$\mathcal{C}(x) = \sum_{g=1}^G \omega_g C_g(x)$$. Sure, I didn't need to use $$\mathcal{C}$$. I could have used anything, $$f,g,$$ etc. But I like that $$\mathcal{C}$$ suggests to the reader that there's a relationship between it and and the family of component functions $$C_g$$.

Question: is there a better way to indicate a function is an aggregate of a family of sub-functions? If no standard, maybe someone has seen an alternative? Maybe there's an approach out there preferred to using \mathcal as I've done above?