void Main()
{
    var x = new foo<bar>();
}
public class foo<T> : IKeyedByObj<T>
{
    public T Key { get; set; }
    public TimeSpan StartTime { get; set; }
    public TimeSpan EndTime { get; set; }
}

public class bar { }

public interface IKeyedByObj<T>
{
    T Key { get; set; }
    TimeSpan StartTime { get; set; }
    TimeSpan EndTime { get; set; }
}