A conical hat has a wide brim that keeps off both rain and sun.
Tips
usage
斗 here is dǒu, the old grain-measuring vessel, wide at the top and narrow at the bottom; the hat has the same shape turned upside down. It is not dòu 'to fight', the reading in 斗争.
culture
A fisherman in a 斗笠 and a straw cape, 蓑衣, is a classic image of the recluse in Chinese painting and poetry.