MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

CREATE TABLE IF NOT EXISTS categories (
    category_id int(11) NOT NULL AUTO_INCREMENT,
    name varchar(255) NOT NULL,
    parent_id int(11) DEFAULT NULL,
    created_at timestamp NOT NULL DEFAULT current_timestamp(),
    PRIMARY KEY (category_id),
    FOREIGN KEY (parent_id) REFERENCES categories(category_id) ON UPDATE CASCADE ON DELETE CASCADE
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4;

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T1', null);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T2', null);

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T11', 1);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T12', 1);

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T111', 3);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T112', 3);

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T1121', 6);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T1122', 6);

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T121', 4);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T122', 4);

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T21', 2);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T211', 11);
INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T212', 11);

INSERT INTO categories (`name`,`parent_id`) VALUES ( 'T2111', 12);

category_id	name	parent_id	path
1	T1	null	T1
2	T2	null	T2
3	T11	1	T1 -> T11
4	T12	1	T1 -> T12
11	T21	2	T2 -> T21
5	T111	3	T1 -> T11 -> T111
6	T112	3	T1 -> T11 -> T112
9	T121	4	T1 -> T12 -> T121
10	T122	4	T1 -> T12 -> T122
12	T211	11	T2 -> T21 -> T211
13	T212	11	T2 -> T21 -> T212
7	T1121	6	T1 -> T11 -> T112 -> T1121
8	T1122	6	T1 -> T11 -> T112 -> T1122
14	T2111	12	T2 -> T21 -> T211 -> T2111