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There are lots of different approaches, levering or tapping the loose ends apart. Maybe a box spanner would work on that nut.
As others have said though, good luck finding a ceramic cartridge that fits. I know some guys carry a set of them and there's a plumbers merchant near me that has a lot of different ones. Occasionally I've had some success but usually with shower mixers not taps.
I’ve tried pulling that out. It will not budge