I have a question regarding notation.

In the equation below, is it fair to say that the sign "\\(+\\)" has two meanings?

> \[ (2 [\textrm{egg}] + [\textrm{yolk}]) + (3 [\textrm{egg}] + 3 [\textrm{pie crust}]) = 5[\textrm{egg}] + [\textrm{yolk}] + 3 [\textrm{pie crust}] \]

For example, if we were to be more explicit we could re-write the equation such as:

\[ (2 [\textrm{egg}] +_1 [\textrm{yolk}]) +_2 (3 [\textrm{egg}] +_1 3 [\textrm{pie crust}]) = 5[\textrm{egg}] +_1 [\textrm{yolk}] +_1 3 [\textrm{pie crust}] \]

- \\(+_1\\) is a way of combining elements from \\(S\\) (?)

- \\(+_2 : \mathbb{N}[S] \times \mathbb{N}[S] \rightarrow \mathbb{N}[S]\\) is the monoidal operation.

In the equation below, is it fair to say that the sign "\\(+\\)" has two meanings?

> \[ (2 [\textrm{egg}] + [\textrm{yolk}]) + (3 [\textrm{egg}] + 3 [\textrm{pie crust}]) = 5[\textrm{egg}] + [\textrm{yolk}] + 3 [\textrm{pie crust}] \]

For example, if we were to be more explicit we could re-write the equation such as:

\[ (2 [\textrm{egg}] +_1 [\textrm{yolk}]) +_2 (3 [\textrm{egg}] +_1 3 [\textrm{pie crust}]) = 5[\textrm{egg}] +_1 [\textrm{yolk}] +_1 3 [\textrm{pie crust}] \]

- \\(+_1\\) is a way of combining elements from \\(S\\) (?)

- \\(+_2 : \mathbb{N}[S] \times \mathbb{N}[S] \rightarrow \mathbb{N}[S]\\) is the monoidal operation.