催 sponsor

I SIGHED when they told me the cost of sponsoring the event.

The person sponsors a turkey roast on top of the mountain.

sponsor ★★☆☆☆ NP
主 (master/mainly) + 催 (sponsor) = 主催 (sponsor)

sponsor a medium party or company event (like 催す（もよおす） but the emphasis is on 'sponsor' (i.e. provide money in exchange for publicity), where as もよおす has more to do with actually doing the work - arranging the chairs and snacks and sweeping the floor, and so on).

repeatedly request ★☆☆☆☆
催 (sponsor) + 促 (peer pressure) = 催促 (repeatedly request)

to repeat and repeat a demand. Can be used about corporations (This is your 3d notice of overdue library book) or between frends, ('I keep asking you to repay that $5 I lent you')

host the Olympics ☆☆☆☆☆
開 (open) + 催 (sponsor) = 開催 (host the Olympics)

host a big event like the Olympics