Custom query: Get all posts that are from a certain category?

Question

it’s quite easy:

$months = $wpdb->get_col("SELECT DATE_FORMAT(post_date_gmt, '%m')
                            FROM $wpdb->posts
                            LEFT JOIN  $wpdb->term_relationships  as t
                            ON ID = t.object_id
                            WHERE post_type="post" AND post_status="publish" AND t.term_taxonomy_id = 11
                            AND DATE_FORMAT(post_date_gmt, '%Y') = $y
                            GROUP BY DATE_FORMAT(post_date_gmt, '%Y-%m')
                            ORDER BY post_date_gmt DESC");

term_taxonomy_id is the category. And I join on the object ID