Karadox

SuperBrain is the het ship between Kara Zor-El and Querl Dox from Supergirl.

Canon
Kara wakes up in her loft, hearing a knock at the door. She opens it to reveal Querl standing there. He talks nervously about how she was talking to him. Kara is very confused by his comments till he calls her Supergirl. She immediately pulls him into the loft telling him to be quiet. He officially introduces himself as Brainiac 5, that his name is Querl Dox, but that the Legionairs just call him Brainy. Kara asks if Mon-El sent him. He replies yes, and that he has to make sure her brain is intact. He comments on how healthy it is despite her being in a coma. Kara is confused by his statement. Brainy tells her that she's been in a coma for two days. She becomes more confused, since she's very clearly in her loft. Brainy explains that the loft is just a physical manifestation of the place where she feels most comfortable. Kara asks how he's with her, if she's in a coma. He explains that he was awoken from the sleep chamber in order to communicate with her, citing 31st century technology as to why he's able to do this, and how it's also keeping her alive. She becomes confused again, Brainy having to remind her that Reign nearly killed her. She becomes panicked as she needs to wake up so that she can stop Reign from hurting anyone else. She goes to the loft door trying to open it, but it stays closed. She continues, becoming more frustrated with the task. Brainy suggests that she relaxes, but she ignores him.

Brainy looks around the loft while Kara sits on the couch, describing being locked in her head as torture. Brainy admits that in all the ways he imagined meeting her, she never described it as torture, then continues looking around. She asks why he's looking around, and he explains that he's checking for brain damage, which would manifest itself as damage in the loft. He needs to check to make sure she's ready for reality re-entry. Kara asks if that means she is ready to wake up, Brainy confirming so. She grins enthusiastically while laughing as she trows a pillow at him. He catches it nonchalantly. Kara asks what she needs to do to get out of the coma. Brainy comes to the conclusion that since the door is the only available exit, all she needs to do is open it. She tries the door but it doesn't open. Brainy then tries the door, but it doesn't open for him either. This confuses him, as he informs her that she should be fine.

Kara continues trying to open the door, becoming more and more frustrated. As Brainy makes tea in the kitchen, he informs her that her body is fine, since the tank heeled it and there were no side effects. He comes to the conclusion that the problem is mental, meaning that she's not letting herself leave. Kara doesn't think that makes sense, given that she's the once that wants to leave. She asks why the door opened for her earlier, Brainy then explaining that it was too let him in, and that her getting out is more difficult. She punches the door, while Brainy asks if there would be any reason as to why her subconscious wouldn't want her to leave, suggesting self preservation. Kara says that she isn't afraid, but Brainy responds that she was badly beaten, and that fear would be a logical response to such an event. She then uses her heat vision on the door. Brainy stares at her, as her heat vision destroys the room around her.

Kara starts cleaning the loft, Brainy wondering why she's doing it, since it's not real. Kara doesn't know, only that she like putting things back in order. Kara realizes that she chose everything in the loft, and that there's probably something in there that her subconscious wants her to see. Brainy that it isn't a bad idea, and wonders why he didn't think of it. Kara then begins to search through her stuff. Kara eventually finds a picture of herself and a black cat. Brainy asks if that was her pet, Kara says yes, but quickly wonders why her subconscious would want her remember her cat. Brainy says it could be a random neuron firing and asks the name of the cat. Kara named him Streaky and that he had been a stray like her. She had found him on her street right after she had come to earth. Brainy asks if she had felt an emotional connection with the cat. Kara says yes, she and Streaky were friends. Streaky suddenly appears on one of the chars in her loft. As she walks over to him, she explains how she used to feed him every night, but was so scared to touch him due to her super strength. She had practiced being gentle, until she was confident that she wouldn't hurt him. She then pet him, and he purred, the act making her feel human, instead of like an alien. Brainy watches her as she pets Streaky, fondness in his eyes.

Brainy accidentally talks about the battle against Reign while in Kara's head. He tries to brush it off as a small fight, and wants her to keep talking to keep his mind off the battle. But Kara says that he should be entirely focused on the battle. Brainy says he's capable of doing both, but shows his strain when he stops mid sentence to tell Mon-El to evade one of Reigns attacks. Kara tells him to go help the legion instead of her. As he's about to leave, he says that it looked like Supergirl had a great life. Kara says that, the stuff in the loft weren't Supergirls, but Kara Danvers'. Brainy tells her how Alex said something similar. Specifically that Kara Danvers was her favorite person. He leaves to join the battle, Kara thinking over his words. She then wakes up and fights Reign alongside the Legion and J'onn.

After Kara checks on Mon-El and Imra after the battle, Brainy walks in her direction. Kara see's him and says hi, then asks if he's shorter in reality. He then asks if she's suggesting that he changed his height while in her head so that she would see him as someone more stable and trustworthy, thereby making her more likely to want to work with him to help her. Kara confusingly answers yeah, and Brainy confirms that she's correct. She laughs, and he says that it's nice to meet her in real life. As he walks away she smiles at him.

Fanon
AO3

Trivia

 * In the Justice League Unlimited episode, Far From Home, the legionairs bring several Justice League members into the 31st Century, including Supergirl. She and Querl meet and fall in love. She decides to stay with him in the future instead of returning to the 21st century.
 * Querl's design in Supergirl is more based on his design from this episode instead of the design from the comics where he's green.