Does Catholicism teach that Trinity is reflected in Man? This question is highly related to, but not exactly a duplicate of 

Does Roman Catholicism teach that man is body and soul (bipartite) or body, soul, and spirit (tripartite)?

The answer to the linked question states a bipartite union:


  according to Catholic teaching, man's one nature is the union of spirit and matter, soul and body.


Genesis 1:27 says:


  God created man in his own image


If God is three persons, shouldn't that mean that man is tripartite as well? Or at least that the Trinity of God is somehow reflected in man? Does Catholic literature discuss this anywhere?

This question comes from the personal experience of having three contradictory wills: the desires of the body, emotional wishes, and what the mind considers right.
St. Thomas Aquinas discusses the question "Whether in creatures is necessarily found a trace of the Trinity?" in his Summa Theologica I q. 45 a. 7. He writes:


  …the processions of the divine Persons are referred to the acts of intellect and will, as was said above (q. 27). For the Son proceeds as the word of the intellect; and the Holy Ghost proceeds as love of the will. Therefore in rational creatures, possessing intellect and will, there is found the representation of the Trinity by way of image, inasmuch as there is found in them the word conceived, and the love proceeding.