nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyzc3f2ytrz5rg45adl0x43zn3cldeusm8j6fpst2u4tl5z0xvdlk2rj4x5t (nprofile…4x5t) I've been calling it a Tambara comodule, I wrote a tiny stub about it here, I noticed the connection to traces but didn't write about that part yet
https://julesh.com/forest/000D/index.xml
An equivalent but less slick definition plays a big role in an old paper of mine, "The game semantics of game theory", I called it something like a "context functor" back then