I always had this wild scenario in my head (way before rooftop at all) of Luffy being in front of Big mum, trying to fight her, but being still overwhelmed. But then the rest of the BM Pirates appear, Big Mum laughing, wanting to finish Luffy, but gets blocked by Katakuri. Everyone there is shocked, the strawhats, Luffy, Big Mum, Big Mum Pirates... but then Katakuri is confronting her.
He is stating he takes over the Big Mum Pirates and he wont allow her to hurt any more of his siblings. While Linlin firstly gets mad, starts the to laugh and ask who is following him anyway. He couldnt even beat Strawhat and now he tries to claim her title? Who does he think he is. He cant take BM down!
Then, while all hestitating and are shocked about Katakuris behavior. Brulee starts coming from the backside and stand directly behind Katakuri. She claims he is right and he will stick to her brother, whatever comes. He was always the better leader. She claims that the island and the crew were in way better state without her and all what brings her up and makes her important is her power. But a new generation is coming up, and the old power wont matter anymore.
Followed by this words, Oven is coming over too. And after him one after another coming to Katakuris side. Till the end Persospero is refusing, calling them, broken heartly obviously, traitor and they shall say sorry. Big Mum was always their connection and she is their mother. Katakuri looks that in direction of Perospero and whispers: "Sorry... for doing this to you Pero...". Perospero is shocked and overwhelmed. And then big mum is attacking Katakuri, while he was focused on Peros. But her attack gets blocked by Pero and Luffy.