The "Kampaku" mentioned in this entry is the Toyotomi Hideyoshi (1536-1598), one of the warlords who unified Japan at the end of the 16th c. In 1592, he launched an attack to Korea, with the ultimate goal of conquering China, and perhaps even India. This fact is proved by some letters he personally wrote during the 1590's, and it is interesting how Ming intelligence was aware of Hideyoshi's ultimate goal already in 1593. Hideyoshi, who never went to Korea, died in 1598. His men, by then stalmated in the South of the Korean peninsula, returned immediately to Japan after seven years of frustrating attempts to submit the local populace. The intervention of the Ming Celestial Army was crucial in repelling the invasion, while the Korean contributed to the defense of their country with successful guerrilla-style attacks both on the land and at sea.
Details on the title "Kampaku" (=Imperial Regent) and about the campaign in Korea can be found in "Hideyoshi," by Elizabeth Berry, 1982; the letters discussing Hideyoshi's ambitions are translated into English in "101 Letters of Hideyoshi," by Adriana Boscaro, 1975.
The campaign in Korea is treated by Jurgis Elisonas in "Japan’s Relationship with China and Korea" in The Cambridge History of Japan, Vol. IV.
As an undergraduate, I wrote a short paper which can be of interest as a simple introduction to this topic. It is still available online at: http://www.samurai-archives.com/hak.html
More sources (Japanese diaries, Korean sources) can be easily found.
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