TeruSigma

"Her eyes are like mine… No, even stronger…"

- Sigma’s thoughts about Teruko in Chapter 76

TeruSigma is the het ship between Sigma and Teruko Okura from the Bungou Stray Dogs fandom.

Canon
Sigma first met Teruko during the latter's infiltration at the Sky Casino in order to hunt down the Armed Detective Agency and inform him about an infiltration of terrorists.

Anime and manga
The Hunting Dogs acquire a lead that the Agency members Atsushi Nakajima and Kyouka Izumi and their ally, Lucy Maud Montgomery, headed to the Sky Casino. Teruko and Michizou Tachihara are then dispatched to the airborne casino where they meet Sigma. Teruko tells him that the casino is infiltrated by terrorists and Lucy is their ally who used her ability to to hide with Atsushi and Kyouka in his casino. Sigma tells her that he can send a team to search them but Teruko replies that it's useless and starts explaining to him the importance to close down the casino while locating the terrorists. Not wanting his casino's affairs to be put on hold, Sigma refuses to blockade the casino. Then, using his employees, Sigma threatens her and Tachihara with directional resonance gun. Explaining that those guns are used against ability users and If they won't leave, he is gonna use it to them. Teruko gets angry to him but leaves with a smile. Later, she steals a gas bottle from his kitchen and blows up the entrance to his casino leaving Sigma in shock.

Alone, Sigma contemplates what to do with Hunting Dogs and that because of Teruko's constructed explosion, they might learn the secret of his casino which makes him to worry. He realises that the only way to keep his secret is to kill them.

After Sigma tried to kill Tachihara with explosive coins, Teruko realizes the reason why Sigma wanted them to leave is because of those coins. At one point, they are surrounded by armed workers and engage them in battle, but Teruko enjoys this battle and wins, which makes Sigma angry. Sigma starts to resort to extreme measures and announces a reward for those who can hurt or kill them, knowing that they, being police officers, will not harm people. Teruko tells Tachihara that Sigma is right and he knows what he's doing but despite of this, they will reach their goal.

When they run away from the casino visitors, Teruko tortures one of the workers and asks him about how they can take control over the central telecommunication terminal. She finds out that only Sigma has the activation key. Then, Teruko tells Tachihara to take care of the guards while she is in meeting with Sigma.

Sigma and Teruko meet eyes and Teruko asks with a smile if he is prepared to surrender. Sigma denies it and Teruko replies him that she won't wait long and she will get to destroy the transmission machine to save the world from blow up by coins. Sigma warns her that it won't change anything and the only way to stop it is using a key, which he tosses to Teruko. Sigma understands that it's impossible for him to win but determined to fight for his casino, Sigma brings forth the Painless Gun and fires a barrage of high-speed 7.62 mm ammo. Teruko, with her enhanced strength, repels the bullets with her bare hands. It makes Sigma very surprising because this machine fires 100 bullets per second and even for Hunting Dogs' body it should be unreal. Soon she attacks the turrets' muzzles with two kitchen knives which she stole from his kitchen.

Sigma attempts to take out a tablet to activate a new set of turrets, but Teruko kicks down his hand and pinning him to the wall, preventing his plan. Cornering him, Teruko urges him to surrender, more so because he has no chance of winning ever since the start. Sigma agrees to how average he is from his conception and and that he isn't a man for fight. Then, he asks her if she understands the feeling of empathized by nobody and loneliness. Teruko answers no and then with serious and determined face, Sigma pulls out a Directional Resonance Gun with his free hand and imparts a final statement that everything has gone as planned.

Sigma pins down Teruko down the ground. He indignantly fires at her. He tells her that it's the strength of his feelings. However, Teruko stands back up and asks him why he thinks that he's the only one who has this feeling, much to Sigma's surprise. She then rushes towards him and grabs his resonance gun. Sigma also notices wounds in her ears, deducing that she must have gauged out her ear canal as a countermeasure.

Teruko explains that the Hunting Dogs undergo rigorous and inhuman procedures to achieve their enhanced physical bodies and if they skip a single one, they will die. It makes Sigma very shoked and he asks her about the reason of why she is going so far. Teruko answers that without order, people "built for violence" will destroy the world so, they are as Hunting Dogs are ready for this, even If they gonna die because of it one day. Then, she breaks his resonance gun. Noticing her determination, Sigma realizes that her eyes are like his own and even stronger as he also did go so far for his casino like she for the order in the world.

While Sigma dropped his guard, Teruko grabs Sigma by his neck and breaks him through the wall, holding him at the edge of the casino. For the last time, she orders him to give up or she's gonna drop him. Sigma refuses and claims that an ordinary man can overcome any wall with enough desperation, though Teruko asserts that beyond that wall is a battle with equally desperate geniuses. Sigma uses his ability on her and becomes very surprised by what he sees. It's some people. They are Fyodor, Dazai, Chuuya, Fitzgerald, Fukuchi, Tetchou, Jouno and her. Currently, it's unknown what does it mean and what he have shown to Teruko, but Sigma becomes sad of it and he agrees with her words.

However, wanting to protect at least the casino over himself, Sigma grabs Teruko and jumps off the edge of the casino to die with her. While they are falling, Teruko tries to reach the outer wall but Sigma prevents her. She wonders where he get this strength, then she gets that it's not an ability, it's his merely desperation. Knowing that she will never take him alive as she planned, she pushes him away to not let herself die. Teruko manages to break free from his hold and grabs on a ledge. Meanwhile, to her shock, Sigma is saved by Atsushi, and they land on an electric power installation box, where Atsushi interrogates Sigma through Ango Sakaguchi.

Differences and similarities between those two
Sigma and Teruko shown to be very different from each other. For example, in terms of choosing clothes, outlook on life and battle tactics. Teruko dresses in a strict military uniform, while Sigma prefers something bright and stylish. Their outlook on life is shown to be unlike each other. Teruko adds that she doesn't understand him at all. If we go to their battle tactics, Teruko prefers to fight hand-to-hand, while Sigma uses weapons and visitors to his casino as help by giving them promises that they will be able to repay their debt.

Despite of this, they share some similarities. The most interesting thing is their indeterminate in age. Sigma was created 3 years ago by The Book, but he looks and thinks like a young man on his 20's. Teruko can change her own and others age by her ability. This makes wonder, if Teruko's ability would have work on Sigma or not. Sigma admits that he is not a great example of masculinity, but tries to become better and find his own way of life. Teruko is not a great example of femininity because of her personality and acting boyish. They are both brave ones who are ready to sacrifice their lives and go to great lengths for their goals.

Fanon
TeruSigma isn't very popular ship in the fandom. People started shipping them after the Sky Casino Arc when those two fought against each other. Mostly, this ship get people's attention more in anime adaptation than in manga.

Currently, there's 5 works for the ship in Ficbook while in AO3, the couple has only 1 romantic work and 1 friendship. Also, there are some people who posted their fanfictions of them in different groups in VK and the number of works is seen to be 11 but can be more.

The rival ships are GogSigma, Sigzai and SigmAtsu on Sigma's end, while Teruko's rival ship is TachiTeru.

Fandom
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Trivia

 * Sigma and Teruko are both characters with indeterminate in age as Sigma was created by The Book and Teruko can manipulate her age by ability.
 * In manga, Sigma states that he finds Teruko's eyes similar to his own that expresses strong emotions. However, in anime it wasn't shown.