冠 has two readings. The first-tone guān is the noun 'hat / crown': 皇冠 (crown), 衣冠 (attire), 冠心病 (coronary heart disease). The fourth-tone guàn is the verb 'to cap / be first': 冠军 (champion), 夺冠 (to win the title).
memory
Object stays level (first tone) guān = the hat itself sitting on the head; action drops (fourth tone) guàn = the act of placing the crown on, hence 'to be ranked first', 冠军.
Top cover radical, a flat lid with two short downward hooks, picturing a cap pulled over the head. This is the indexing radical for 冠 and supplies the core image of headwear, the same lid that crowns 军 and sits over 写.
Middle 元 originally pictures a person with a marked head, meaning head / top / primary. Sitting under the cover and above the hand, it tells you exactly what gets capped: the head. Reinforces 冠 as the highest formal headpiece.
Bottom-right 寸 depicts a hand with a thumb mark, here the hand that places the cap. The full picture: a hand fitting a hat over a person's head. This scene also licenses the verb reading guàn 'to crown', as in champion.
