Контекст:

In addition to writing an introductory summary of his master's theories (the treatise entitled Launching-Points to the Realm of Mind), Porphyry also composed the famous Isagoge, an introduction to the Categories of Aristotle, which came to exercise an immense influence on Mediaeval Scholasticism.

Источник: http://www.iep.utm.edu/neoplato/

Кажется, речь идёт об оказании огромного влияния, но непонятно, чем это по смыслу отлично от, скажем, which had exerted an immense influence on.