Right
斗 — a pictograph of a long-handled dipper used as a unit of dry measure (about 10
升). Reinforces the meaning:
科 is etymologically 'measuring grain with a dipper', the act of sorting and grading harvests. By extension came 'category, branch, department, exam-classification' — every modern sense of
科 (
科学 science,
科目 subject,
内科 internal medicine) traces back to 'sorting things into measured portions'.