Add a extra category attribute under general infomation tab

Try it like this:

$installer->addAttribute('catalog_category', 'nav_left', array(
    'group'         => 'General Information',
    'type'     => 'int',
    'label'    => 'Show in left navgigation',
    'input'    => 'boolean',
    'global'   => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_STORE,
    'visible'           => true,
    'required'          => false,
    'user_defined'      => false,
    'default'           => 0
)); 

EDIT
$installer must be instance of Mage_Catalog_Model_Resource_Setup.

Off topic a bit: I recommend adding this script in an update file of one of your modules instead of making an instance of Mage::app() and running it 'on the fly'. If you put it in an upgrade script it's portable to other instances.

I have managed it work in expected way like this.

$installer->addAttribute('catalog_category', 'left_nav',  array(
    'group'    => 'General Information',
    'type'     => 'int',
    'label'    => 'Show in left navigation',
    'input'    => 'select',
    'global'   => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_STORE,
    'visible'           => true,
    'required'          => false,
    'user_defined'      => false,
    'default'           => 0,
    'source' => 'eav/entity_attribute_source_boolean'
));

Thanks