MuiYuu

"The truth is I knew. The "Mu" in "Muichiro" is the "Mu" in "Mugen". Infinity."

- Yuichiro to Muichiro, chapter 118

MuiYuu is the family ship between Muichiro Tokito and Yuichiro Tokito from the Demon Slayer fandom.

Canon
Yuichiro and Muichiro are twin brothers. Yuichiro and Muichiro are different since Yuichiro has a more cold and negative outlook on life, while Muichiro is more emotional and kind hearted. They live with their parents in a cabin in a forest near a small river. Their father is a woodcutter and the two of them are seen helping him. They are also seen playing together at the small river.

When they were ten their mother caught a cold which developed into bronchitis, due to this their father went out to look for medicine. However, since this was during a rainy day he slipped and fell to this death. From that day on they only had each other, since their mother died that very same day. The two of them continued to cut wood. At some point the twins came across Amane, who asked them if the two of them wanted to join them. Muichiro was excited about this, however Yuichiro was not and rejected what Amane offered for the both of them and sent her away. After this Yuichiro had an outburst, which revealed that he blames their parents dead on their parents nature. This led to Yuichiro adopting a cold demeanor, as he hopes that it keeps him and Muichiro alive. Amane, however, continued to visit them and each time she visited Yuichiro chased her away.

When they were eleven they left the door open at night, due to the warm weather. Yuichiro was sleeping while Muichiro was drinking some water, during this a demon entered their cabin then said something and went to attack Muichiro. Yuichiro awoken by the demon yelled out Muichiro while jumping in front Muichiro to protect him. This however, caused Yuichiro to lose his arm. As a reaction to this Muichiro yelled out with tears in his eyes Yuchiro while holding his brother. Muichiro while holding Yuichiro backs into a corner of a wall with a terrified expression in his eyes. The demon talks about something and is seen smiling and laughing. The scene shifts where we first see a dying Yuichiro laying down and then to a scene where Muichiro, who has no spark in his eyes, is seen with a very beat up demon at sunrise. Right after that Muichiro drags himself back to Yuichiro. Muichiro sees Yuichiro laying there and proceeds to grab a hold of Yuichiro’s hand. While Muichiro is doing this Yuichiro is praying to the heavens for someone to help his brother and that Muichiro might survive. Muichiro continued to lay there while grasping his brother's hand, even after Yuichiro passed away. Eventually the two were separated when Amane arrived and went on to heal a severely wounded Muichiro. Due to this event Muichiro lost his memories.

During Muichiro’s fight against Uppermoon 5: Gyokko in the swordsmiths village arc, he gets trapped by one of Gyokko’s vases. With this trap being a bubble of water, where Muichiro is left to drown. During this Muichiro remembers his father, because of something that Tanjiro said. This led to Muichiro remembering his family again. The flashback shows Muichiro standing “alone” before his parents, since he at first thought he was an only child but then he remembers that he has an older twin brother. He also remembers the rest of his past, including his anger over Yuichiro’s death and that Yuichiro said that the “Mu” Muichiro comes from “infinity”. The regaining of his memories caused him to unlock the demon slayer mark. After the battle was over and fell unconscious for a bit, this caused him to see his family and thus Yuichiro again. During this sequence they talked with each other for a short moment before Muichiro gained consciousness again.

In the infinity castle arc, Muichiro is up against Uppermoon 1: Kokushibo. During the battle Kokushibo slices Muichiro in half, killing him. Later Muichiro’s open eyes were closed by someone else and then it shows Muichiro opening his eyes again in a different place where he is surrounded by yellow/goldish leaves and sees Yuichiro again standing before him. And thus the two of them reunite again.

In chapter 205, we see that Yuichiro and Muichiro are reincarnated as a pair of newborn twins.

Fanon
The twins are often portrayed in fanart together surrounded by yellow/goldish leaves. Many fans also feel bad for the twins as to what happened to them, some create an AU where both of them get to survive.

Fandom
FAN FICTION