Final answer:
The key events in the cell cycle that are monitored inside the cell are DNA damage and replication completion, centrosome duplication, and assembly of the spindle and attachment of the kinetochores to the spindle.
Step-by-step explanation:
The key events in the cell cycle that are monitored inside the cell are DNA damage and replication completion, centrosome duplication, and assembly of the spindle and attachment of the kinetochores to the spindle. These events are assessed at different checkpoints throughout the cell cycle. The integrity of the DNA is assessed at the G1 checkpoint, proper chromosome duplication is assessed at the G2 checkpoint, and attachment of each kinetochore to a spindle fiber is assessed at the M checkpoint.