[dwohnitmok]

函子 should probably be analyzed as an abbreviation of "函数" (function) + "子" ("essence of" or "atomic unit of"). This meaning of "子" is the predominant one when used in technical contexts. See molecule "分子" （unit of separation） atom "原子" (the original/fundamental unit) electron "电子" (unit of electricity) or monad "单子" (essence/unit of oneness) where the second character is third tone not neutral. Many of these originate in Japanese and are re-borrowed back into Chinese, but that's a story for another time.

A sibling comment points out that 子 can mean child. This is the original, ancient meaning of the character. This usage is still productive in modern Chinese (usually to mean sons), but the previous examples are examples of how the meaning has undergone some transformations to form derived, related meanings. The original meaning can also be found in technical contexts. Examples of this are 子集 (child + set = subset) and again 分子 (fraction + child = numerator) with the counterpart 分母 (fraction + mother = denominator). This is not how I scan functor 函子 though.

In the Chinese programming community, you'll usually just see the English words "Functor" and "Monad" used. I wouldn't be surprised if some Chinese programmers familiar with "Functor" do not recognize "函子." I've only ever seen 函子 used in math articles and occasional FP tutorials (and even then, given how dominant English is, it is often glossed by "Functor").