Okay, sounds good. I think people sometimes use \$$\mathrm{Disc}(S)\$$ for the [discrete category](https://en.wikipedia.org/wiki/Discrete_category) on the set \$$S\$$, and people definitely use \$$n\$$ to mean the set \$$\\{0, \dots, n-1\\}\$$, so we could also call this category \$$\mathrm{Disc}(n)\$$... which is almost what you wrote!