Why is it impossible to use IList <T> in an interface definition and List <T> in an implementation?

Question

Why is it impossible to use IList in an interface definition and then implement this property using List? Am I missing something here or is the C # compiler just not resolving this?

public interface ICategory
{
    IList<Product> Products { get; }
}

public class Category : ICategory
{
    public List<Product> Products { get { new List<Product>(); } }        
}

the compiler says that error 82 'Category' does not implement the interface member 'i. category.Products'. "Category. Products" cannot implement "ICategory.Products" because it does not have the appropriate return type "System.Collections.Generic.IList"

Answer 1

, . , , API. -, :

public interface ICategory
{
    IList<Product> Products { get; }
}

public class Category : ICategory
{
    IList<Product> ICategory.Products { get { return Products ; } }
    public List<Product> Products { get { ...actual implementation... } }        
}

Answer 2

:

public interface ICategory
{
    IList<Product> Products { get; }
}

public class Category : ICategory
{
    // Return IList<Product>, not List<Product>
    public IList<Product> Products { get { new List<Product>(); } }        
}

.

Answer 3

It will work

public interface ICategory<out T> where T:IList<Product>
    {
        T Product { get; }
    }

public class Category : ICategory<List<Product>>
    {
        public List<Product> Products
        {
            get
            {
                throw new NotImplementedException();
            }
        }
    } 

Although difficult, but possible.