The Red Fire Truck or Red Apple Tree?

The notion of mapping between the maps, or having some structure to what all those maps are. The very fact that red maps into all thesek phrases, like red fire truck or red apple tree, om, it's like the structure you want to study. And then that motivated a math question, which we think has a really nice answer in the language of category theory. So here i'm thinking, my arrow that goes from red to red fire truck. That's like there's an arrow. It's a set with one element, the one element being the one arrow. And indicates red sits inside o, red fire truck, right? But maybe there's like a statistical story to that