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Izuku's death didn't change him.
He was still brash, still victorious, still eager to prove that he could be better than All Might. He worked himself to the bone, keeping up with his training and his paperwork, making sure he stuck to his schedule and deadlines, not letting the capture of villains take too long so he didn't work too much overtime.
He stayed focused. He stayed on track.
Katsuki lies awake at night, past his bedtime, and wonders if Izuku would be proud of him.
His friends and coworkers mourned, of course. Wore white and set out offerings, as if Izuku could see them, could eat the food, could participate in life again.
Katsuki didn't leave an offering, wore a white shirt and lit a stick of incense, his only nod to tradition. He was quiet, observed the ceremony without a word to anyone, and left when it was done.
He was back at work the next day, cursing at his coworkers for failing to submit their paperwork on time.
The red-lined eyes of his coworkers could only reflect their surprise and hurt of his behavior — of his lack of care.
Katsuki reads through the notebooks Izuku left behind, reads them chronologically and sees how Izuku's analytical skills only got better as he interacted with heroes and fought actual villains.
He doesn't read the notebooks about himself.
Villains liked to use Izuku's death as a taunt, as a way to rile him up. He wondered why they continued to try when it never bothered him, when their words about the lack of Deku didn't faze him, when he still captured them and handed them over to the relevant authorities.
He thought it a waste of time.
Izuku's death didn't hurt him, not like it did the others. He didn't take a moment to catch himself in midair and reel from the hurt villains thought he would feel. The wound had never opened, and therefore never scabbed.
He was unmarked.
Katsuki spends hours in the gym, constantly pushing himself, increasing his reps and weight, competing with someone who doesn't exist anymore.
His tears blend with his sweat and he grits his teeth.
He realizes how much of a popularity game the hero industry is, how the underbelly of his profession is something not taught in a class but only learned about when interning. He learns that having everything recorded is a double edged sword and that it's difficult to remain true to oneself when people are eager to criticize every blink.
It's a new challenge, one he learns to live with, one he learns to overcome.
Katsuki stares into his food and wishes he could still hear the rambling of a green-haired boy, one he was only beginning to appreciate. He regrets the years spent bullying him, spent trying to overcome his own issues on someone who didn't mind taking the burden, who was only trying to be a hero in the purest sense.
Katsuki holds his chopsticks tightly and screws his eyes shut, not wanting to cry, not wanting to see the truth around him, not wanting to be aware of the void that now existed in his life.