A person or thing that continues something, especially a work, tradition, or legacy begun by someone else.
From continue + -ator (one who does). From Latin continuare, from continuus (continuous, uninterrupted).
Historians use this word for the successors who carried on great works—the continuators of Homer, the continuators of a family business. It's respectful but slightly secondary, like you're important but not quite as original as whoever started it.
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