Depending on whether the mixing adds or subtracts wavelenghts of light we can different additive and subtractive colour mixing. The way rays of coloured light mixes is called additive since we "add" new and new wavelenghts of light to the mix. On the other hand the way pigments mix, that is how we mix dyes is called subtractive since the added matrial will "absorb" more wavelenghts.
Nonetheless both structures are semigroups in my opinion. The underlying set is the set of all possible colours, the group operation is colour mixing in the two different ways, which gives rise to two semigroups. My question would be that is there an isomorphism between these two, the semigroup of dye mixing and the semigroup of light mixing?
To take a extremely simplified model, suppose that you have a set $\Omega$ of "elementary colors" or wavelengths. A color is a subset $C\subset \Omega$. Adding two colors $C$ and $D$ creates the color $C\cup D$, while mixing them the "dye" way creates color $C\cap D$. In this model, there is indeed an isomorphism: complementation satisfies $(C\cup D)^\complement = C^\complement\cap D^\complement$.