For those not familiar with Joachim of Fiore and his three age prophesy:

Joachim Of Fiore, Fiore also spelled Floris, Italian Gioacchino Da Fiore, (born c. 1130, /35, Celico, Kingdom of Naples [Italy]—died 1201/02, Fiore), Italian mystic, theologian, biblical commentator, philosopher of history, and founder of the monastic order of San Giovanni in Fiore. He developed a philosophy of history according to which history develops in three ages of increasing spirituality: the ages of the Father, the Son, and the Holy Spirit.

https://www.britannica.com/biography/Joachim-of-Fiore

Joachim's Three Age Prophecy, which he based on the Christian trinity, saw the age of the Father being the Jewish theocracy, the age of the Son being the rule of the Catholic feudal church, and the age of the holy spirit being a future period of mystic spiritual perfectionism when the Church would be ruled by an Order of the Just. Really, this last age is the universal application of communism which governs the monkish orders, and the Order of the Just are the monks themselves, specifically the Jesuits. An early follower of Joachim tried to identify the Franciscans with the Order of the Just, but unlike the other monastic orders like Franciscans who remain cloistered in monasteries and isolation, the Jesuits operate openly out in the world, working their schemes and machinations, rather than withdrawing from society, while still holding to the ascetic monastic disciplines and the communist vow of poverty, thus eliminating the Franciscans, Dominicans, etc from consideration.

I learned about the Three Age Prophecy from Drake Shelton/Southern Israelite who emphasizes how the philosopher Hegel incorporated Joachim's Three Age Prophecy into his historiography, and how Hegel was a mentor to Karl Marx, to whom Hegel undoubtedly taught the Three Age Prophecy of Joachim as can be concluded from the following:

Reviewed Work: Joachim of Fiore and the Myth of the Eternal Evangel in the Nineteenth Century by Marjorie Reeves, Warwick Gould Review by: Ruth apRoberts The Journal of English and Germanic Philology Vol. 88, No. 3 (Jul., 1989), pp. 445-447 Published by: University of Illinois Press

Remember too that Karl Marx was trained by the Jesuits, and the Jesuits, as is about to be shown, were inspired by Joachim and his Three Ages, believing their Order to be the prophetic Order of the Just.

Southern Israelite has show how the Jesuits based themselves on Joachim's prophecy by citing from page 140 of The Secret Instructions of the Jesuits. Seeing as some people have called this a forgery, I am grateful to have come across quotes by a modern scholar further vindicating this fact; the following citations are taken from E. Randolph Daniel of the University of Kentucky in his review of the book Joachim of Fiore and the Prophetic Future by Marjorie Reeves:

Jesuits believed that Joachim had prophesied the coming of the Society. Benito Pereyra, SJ, used Joachim's thinking in his commentary on the Apocalypse and Joachim influenced Guillaume Postel, who also was a Jesuit.

This one is particularly striking in light of the current and first Jesuit Pope:

Joachim had envisioned a reforming pope as one element in the coming of the third status... But in the Vaticinia this became a series of four messianic popes.

Credit to /u/Veritas__Aequitas.