Final answer:
Cesar Cui was the weakest of the Mighty Five but played a vital role as a music critic, propagandist, and author on the history of Russian music.
Step-by-step explanation:
The composer in question, known for being the weakest of the Mighty Five and a crucial music critic and propagandist for the group, as well as an author on the history of Russian music, is Cesar Cui. Despite not being the most musically gifted amongst his peers, Cui played a significant role in promoting the Russian music of his time and was an integral part of the Mighty Five, a group of composers dedicated to producing a distinctly Russian style of classical music.