"...he has no ambition and no energy. He will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right. Again and again I have taken a problem to him, and have received an explanation which has afterwards proved to be the correct one. And yet he was absolutely incapable of working out the practical points..."
--Sherlock Holmes, speaking of his brother in The Adventure of the Greek Interpreter
Mycroft has appeared or been mentioned in at least four stories by Doyle, including "The Greek Interpreter", "The Final Problem", "The Adventure of the Empty House" and "The Adventure of the Bruce-Partington Plans". While he does occasionally exert himself in these stories on the behalf of his brother, he on the whole remains a sedentary problem-solver, providing solutions based on seemingly no evidence and trusting Sherlock to handle any of the practical details.
In Robert A. Heinlein's novel The Moon Is a Harsh Mistress, the name "Mycroft Holmes" refers to a self-aware computer system entrusted with running the life-support systems, among other things, in a penal colony on the Moon or "Luna". The computer, also referred to as "Mike", eventually sides with characters inciting a revolution to free Luna, and is instrumental in their victory against the Lunar Authority on Earth.\n
In The Moon Is a Harsh Mistress