Is Zagreus a Real God in Greek Mythology?

As the protagonist of Hades, Zagreus received a lot of acclaim from fans and critics alike. His performance as a character was both a power fantasy for many players and an absolute thrill to watch from a performance standpoint. Through Zagreus, players get to experience a world with different perceptions and ideas about love and family, distancing themselves from the prejudices often found in the real world. With all the things Zagreus accomplished during the game though, and all the love fans have for him, the question needs to be asked: Is Zagreus a part of real-world Greek mythology?