Mysql – Make This Query Faster

I have this SQL query:

SELECT parent_category FROM category
JOIN
(
    SELECT category_id FROM venue
    JOIN
    (
        SELECT venue_id FROM city_venues
        WHERE city_id = 3
    ) AS venues 
    WHERE venues.venue_id = venue.venue_id
) AS venue_categories_list
WHERE venue_categories_list.category_id = category.category_id;

This command gives me exactly the results I want but I have noticed that it's execution is very slow (100-200ms) even with small datasets. Since I want this query to be part of a trigger, I want it to be as efficient as possible. Any ideas on how to make this faster ?

EDIT:

The tables related to this query are the ones below:

CREATE TABLE queries:

-- -----------------------------------------------------
-- Table `app`.`category`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `app`.`category` (
  `category_id` CHAR(24) NOT NULL,
  `category_name` VARCHAR(50) NOT NULL,
  `category_plural_name` VARCHAR(50) NOT NULL,
  `parent_category` CHAR(24) NOT NULL,
  `url_icon` VARCHAR(200) NOT NULL,
  PRIMARY KEY (`category_id`),
  CONSTRAINT `fk_parent_category`
    FOREIGN KEY (`parent_category`)
    REFERENCES `app`.`category` (`category_id`)
    ON DELETE CASCADE
    ON UPDATE CASCADE)
ENGINE = InnoDB;


-- -----------------------------------------------------
-- Table `app`.`venue`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `app`.`venue` (
  `venue_id` CHAR(24) NOT NULL,
  `venue_name` VARCHAR(100) NOT NULL,
  `address` VARCHAR(100) NULL,
  `lat` DECIMAL(16,14) NOT NULL,
  `lng` DECIMAL(16,14) NOT NULL,
  `category_id` CHAR(24) NOT NULL,
  PRIMARY KEY (`venue_id`),
  INDEX `fk_venue_category_idx` (`category_id` ASC) VISIBLE,
  CONSTRAINT `fk_venue_category`
    FOREIGN KEY (`category_id`)
    REFERENCES `app`.`category` (`category_id`)
    ON DELETE NO ACTION
    ON UPDATE NO ACTION)
ENGINE = InnoDB;


-- -----------------------------------------------------
-- Table `app`.`city`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `app`.`city` (
  `city_id` INT NOT NULL AUTO_INCREMENT,
  `city_name` VARCHAR(50) NOT NULL,
  `lat` DECIMAL(16,14) NOT NULL,
  `lng` DECIMAL(16,14) NOT NULL,
  PRIMARY KEY (`city_id`),
  UNIQUE INDEX `city_name_UNIQUE` (`city_name` ASC) VISIBLE)
ENGINE = InnoDB;


-- -----------------------------------------------------
-- Table `app`.`city_venues`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `app`.`city_venues` (
  `city_id` INT NOT NULL,
  `venue_id` CHAR(24) NOT NULL,
  PRIMARY KEY (`city_id`, `venue_id`),
  INDEX `fk_venue_idx` (`venue_id` ASC) VISIBLE,
  CONSTRAINT `fk_hasVenues_city`
    FOREIGN KEY (`city_id`)
    REFERENCES `app`.`city` (`city_id`)
    ON DELETE CASCADE
    ON UPDATE CASCADE,
  CONSTRAINT `fk_hasVenues_venue`
    FOREIGN KEY (`venue_id`)
    REFERENCES `app`.`venue` (`venue_id`)
    ON DELETE CASCADE
    ON UPDATE CASCADE)
ENGINE = InnoDB;

I use MySQL Workbench to generate the queries for creating the schema. I use InnoDB as the engine.

EXPLAIN Output:

What I want to do with this query is to return all parent categories IDs' for each venue a city has. I care about duplicates as I want to count how many venues of each category does a city have. I would appreciate if you could give me hints about how I can do multiple counts also ( return columns with each category metrics).