The university fosters an environment that is both socially and intellectually stimulating.

intellectually 是形容词 intellectual 的副词形式，由名词 intellect（智力、才智）加上形容词后缀 -ual 构成形容词，再加上副词后缀 -ly 构成副词，表示"在智力方面"或"从智力角度"。