How is std::function constructed for a lambda

I am a bit confused by how std::function is constructed at a given lambda. The constructor of std::function is listed here. Which one is actually used to capture a lambda? Is it template< class F > function( F f );? Looks like I can't construct std::function with a lambda that captures non-copy-constructible objects. Why is this necessary for lambda capture?

// fu is an object of type std::future 
std::function f = [future=std::move(fu)]() {...}  // compile error

// foo is an object of type int
std::function f = [foo=std::move(foo)]() {...} // compile ok