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Related to stay up: stay up late
stay up (for something)
to remain awake and out of bed for some nighttime event. I will stay up for her arrival. I can't stay up that late.
1. To remain awake: I stayed up all night reading.
2. To remain on display: Their Christmas tree stayed up until February.
3. To remain well informed: They stay up on current trends by reading fashion magazines. I don't know how doctors stay up with all the new research.