write on vs compose

write on and compose both are verbs.

Word	Noun	Adjective	Verb	Adverb
write on	No	No	Yes	No
compose	No	No	Yes	No

As verbs, compose is a hypernym of write on; that is, compose is a word with a broader meaning than write on:

Other hypernyms of write on include indite, pen, write.

write on (verb)	compose (verb)
write about a particular topic	make up plans or basic details for
	produce a literary work
	write music
	put together out of existing material
	calm (someone, especially oneself); make quiet
	form the substance of