Comment by armchairhacker

`Fn`, `FnMut`, and `FnOnce` can also implement and not implement `Sync` (also `Send`, `Clone`, `Copy`, lifetime bounds, and I think `use<...>` applies to `impl Fn...` return types).

EDIT: https://news.ycombinator.com/item?id=46750011 also mentioned `AsyncFn`, `AsyncFnMut`, and `AsyncFnOnce`.