When Laurel Hubbard, a 43-year-old weightlifter from New Zealand, makes her first attempt in the women¡¯s heavyweight competition Monday, she will become the first openly transgender female athlete to compete at the Olympics.

Yet she will do so amid a debate over whether she should be at the Games at all.

Athletes, advocates for women¡¯s sports and fair-sport campaigners have questioned whether Hubbard, who competed in men¡¯s competitions before quitting the sport more than a decade ago, has an unfair advantage. Others believe the Games¡¯ binary categories fail to account for a diverse group of athletes.