I hacked into Mingi's computer and found a photo of him
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Despite the hostility/rivalry the latter maintains toward him, Mycroft cares greatly for his brother, Sherlock, although his ways of watching out for his brother are unorthodox in the extreme. He is an almost entirely socially detached and calculating individual with an exceptional degree of self-control.
After he has first witnessed Sherlock and John working together, he tells his assistant to update Sherlock and John's surveillance status to level 3, implying that he already had governmental surveillance on Sherlock. In tandem with his high intelligence, his self-confidence and mental resilience are almost inhuman, as he seems to be practically immune to even his own brother's probing and he was even able to resist Eurus own ability to instantly reprogram a person despite Eurus being more intelligent. He is, however, not above petty or childish arguments with Sherlock, claiming that the latter's petty feud with him was "childish" and upsetting their mother, and he also argued with Sherlock in front of one of his peers and John in Buckingham Palace to force him to wear pants. Like Sherlock, Mycroft also smokes cigarettes albeit low-tar only, with him carrying a pack at any moment and able to enjoy chatting over smoking, usually without his parents finding out.
Mycroft is shown to be much more capable of faking or maintaining a degree normalcy than his brother, whereas Sherlock is ostracized for his behaviour, Mycroft is highly respected by his peers. Though Mycroft is apparently just as cold as his brother, once informing him categorically that caring was not an advantage, he still strongly reacts to the loss of a human life, as seen in his forced part in Eurus' game at Sherrinford. He refused to take the life of Sherrinford's governor when offered the gun, felt the condemnation game over the lives of the three Garrideb brothers to be insane and inhuman, worried over the imminent death of Molly Hooper's life, and acted to preserve the lives of the people in the city which were threatened by the 'plane' that Eurus had set up.
He is thought to be very lonely and isolated. Sherlock has said this to him too, as even Sherlock has friends but Mycroft has none (that he considers friends at least). Mycroft believes himself to be "living in a world of goldfish", showing how he believes himself to be surrounded by people of much lower intelligence.
However, despite his lack of romantic interests, it is suggested that he is not a virgin unlike his brother Sherlock. When in Buckingham Palace, upon telling his brother not to be alarmed as Irene Adler's job was to do with sex, Sherlock replied "Sex doesn't alarm me," to which Mycroft sarcastically asked him "How would you know?". To make up for his accusation of treason, Lady Smallwood has taken up Mycroft on this regard. On other occasions, Irene Adler had informed the Holmes brothers that Moriarty's nickname for Mycroft was "The Iceman" whereas his nickname for Sherlock was "The Virgin." Also, during the wedding of John and Mary, Sherlock had phoned Mycroft just after Mycroft had finished exercising and asked him why he was out of breath. He then stated that he had either caught Mycroft in a "compromising position" or he had been working out again. He might work out primarily to keep his body healthy and thus his mind sharp as it seems he is quite physically weak. This is demonstrated when he patronizingly referred to Sherlock as "brother mine" and Sherlock effortlessly twisted his arm up his back. John even warned Mycroft that Sherlock could easily injure him severely and Mycroft reluctantly departed, indicating he is capable of picking and choosing his confrontations, a trait Sherlock either lacks or dismisses.
Again, despite his cold and seemingly unsympathetic personality, he cares greatly about his family and those close to him, especially his younger brother Sherlock, as he smiled impulsively upon being surprised by a home video of him and his family as a child, and at seeing a young Sherlock tackle his younger self in a hug. In the first episode he had told John that he "worries about him (Sherlock) constantly." In another episode, Sherlock and Mycroft are seen to be smoking outside their parents' house on Christmas day, where Mycroft says to Sherlock "Your loss would break my heart." Mycroft also cares a lot about John, as in Eurus' last game at Sherrinford of trying to force Sherlock to choose between killing Mycroft or John in order to be granted another chance at saving the 'plane' from crashing into the city, Mycroft, despite the asset his superior intellect would contribute, tries to manipulate Sherlock into killing him over John out of regard for them both, a gesture that Sherlock himself recognized and admitted made it even harder for him to raise the gun. When Sherlock was prepared to kill himself, to wreck Eurus's last game, as well as spare John and Mycroft, Mycroft was shown to be horrified, and stepped forward, as if to try and stop him, showing just how much he cares for his brother. He also cares about his parents very much, as he keeps them informed as to whether Sherlock may have relapsed on drugs and, though definitely misguided, he also lied to them about Eurus and said she died in a fire after being taken away, feeling this was kinder than telling them what she had become (a complete psychopath). This led to their outrage when he finally confessed the truth to them, and Mycroft was very ashamed as they reproached him. However, they forgave him for it, attending a violin recital of Sherlock and Eurus in Sherrinford with Mycroft, wherein his mother placed her hand on his, showing they harbored no animosity for his previous deceit.
In contrast to his relationship with Sherlock, Mycroft's feelings to his youngest sister Eurus were more estranged. Though he recognized the outstanding genius of her superior intellect, Mycroft was aware of Eurus's disturbing personality and actions. Aware of the dangers posed by his sister's psychosis coupled with her abilities, Mycroft supported Eurus's secret institutionalization at Sherrinford with their uncle Rudy's help. Mycroft regards Eurus as a danger first and foremost and conducts himself accordingly, being resistant and unwilling to becoming subject to her manipulations. The mere mention of her, and recalling memories of Eurus, brought even higher guard and dread than even Charles Augustus Magnussen's name. In turn, Eurus had a singular preference for Sherlock and seemingly holds Mycroft with no regard beyond Sherlock's attachment to Mycroft and in comparison with Sherlock's attachment to John. Despite this, Mycroft does hold a measure of sentiment for his younger sister, occasionally speaking to Eurus and exchanging consultations of her genius insight with 'treats' such as a violin and, despite the extreme danger that in part came from it, a genuine unsupervised conversation with Jim Moriarty for five minutes. Though his mother abhorred Mycroft's actions of secretly institutionalizing Eurus for decades, Sherlock recognized that Mycroft had done his best considering everything regarding Eurus. Mycroft also harbors a love for vintage cinema in his home, silently quoting the lines by one of the leads.
Mycroft Holmes (Gatiss) (bakerstreet.fandom.com)