Why I cannot define a Simple Struct with Safe + Send features enabled

This could be a very basic Rust question, I am trying to create a mut static object inside a mod. And to do that I need to implement a Lazy construct but I am not understanding why I cannot create a Lazy construct for my simple struct:

pub struct S {
    a_: String,
}
impl S {
    pub fn new(a: String) -> Self {
        S {
            a_: a
        }
    }
    pub fn foo(&self) {
        println!("{}", self.a_);
    }
}
unsafe impl Sync for S {}
unsafe impl Send for S {}

I am getting errors like:

`error[E0277]: `Cell<Option<fn() -> S>>` cannot be shared between threads safely    --> src/main.rs:26:15
    | 26  |     static X: Lazy<S> = Lazy::new(|| {
    |               ^^^^^^^ `Cell<Option<fn() -> S>>` cannot be shared between threads safely
    |
    = help: within `once_cell::unsync::Lazy<S>`, the trait `Sync` is not implemented for `Cell<Option<fn() -> S>>`
    = note: if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` note: required because it appears within the type `Lazy<S>`    --> /playground/.cargo/registry/src/index.crates.io-6f17d22bba15001f/once_cell-1.19.0/src/lib.rs:714:16
    | 714 |     pub struct Lazy<T, F = fn() -> T> {
    |                ^^^^
    = note: shared static variables must have a type that implements `Sync``

First I tried to define the struct S without the custom impl’s:

unsafe impl Sync for S {}
unsafe impl Send for S {}

But it didn’t work. As in the below code I am adding them back but no results.

fn main() {
    let s = s_mod::S::new("10".to_string());
    s.foo();
}

mod s_mod {
    use once_cell::unsync::Lazy;

    pub struct S {
        a_: String,
    }
    impl S {
        pub fn new(a: String) -> Self {
            S {
                a_: a
            }
        }
        pub fn foo(&self) {
            println!("{}", self.a_);
        }
    }
    unsafe impl Sync for S {}
    unsafe impl Send for S {}
    
    static X: Lazy<S> = Lazy::new(|| {
       let s = S::new("4".to_string());
       s
    });
}

What am I missing here? Can someone help me understand?

>Solution :

once_cell::unsync::Lazy cannot be sent across threads (as implied by the unsync).

You should use once_cell::sync::Lazy instead.

Your struct itself being Sync is insufficient as it is wrapped inside of this type.