Derived complete modules
https://mathoverflow.net/questions/331487/derived-nakayama-for-complete-modules/331501#331501 (see also https://mathoverflow.net/questions/316147/is-there-an-adjoint-to-the-inclusion-of-i-adically-complete-modules-to-all-modul/316197#316197 )

The most important fact about derived complete modules is that they form an abelian category. My feeling is that the "derived complete modules" terminology serves to hide this fact, while my "contramodules" terminology (while certainly clumsy in some usages) is intended to emphasize the fact.

Anyway, I expect to see a lot of confusion around this concept in the near future. I wish my writings could do a better job of clearing up the mess for the rare dedicated reader.