More critically, the mantis shrimp doesn’t have opponency.
In humans—-and most other animals—-the visual system represents color[0] using a relative system: is something redder than it is green? Bluer than it is yellow? To create this, neurons receive excitatory input from (e.g.) a red cone and inhibitory input from nearby green cones. This representation makes sense, given the cones’ spectral sensitivity, but it also makes some colors “impossible”. Since each color is essentially a point along these two axes, something can’t be blue and yellow at the same time, reddish green, or even some shades of “hyper-green”[1,2].
The mantis shrimp, near as we can tell, doesn’t have this sort of representation. The anatomical pathways don’t seem to be there, and some behavioral work with trained(!) mantis shrimp also suggests that they have independent color channels, and, as a result, their color sensitivity is actually not amazing. Interestingly, they may do something to “fake” color opponency: different receptor types are in different parts of the eye, and the shrimp ‘drags’ its eye across the scene to produce a sort of temporal context.
That’s more than you probably wanted to know but...shrimp are neat.
[0] To a first approximation, anyway.
[1] There is a place called Reddish Green, which I assume is not invisible, but I’ve never been to Stockport, England.
[2] More seriously, there are some tricks you can play to (briefly) perceive some of these impossible colors. The general approach is that you stare at something of one color, then quickly switch to looking at something of the opponent color. This “fatigues” (adapts) cells that signal the first color, so they provide less inhibitory input in response to the second color.