mathematics - The etymology of 関手【かんしゅ】

In Japanese mathematics, the word ‘functor’ is translated as 関手【かんしゅ】. What is the etymology of this word?

I suspect that it is a pun on 関数 (function). This leads to two further questions:

1. Why 関手 and not 函手? According to Wikipedia 函数 was standard until the late 1950s. Category theory (圏論) was invented in the late 1940s, and was certainly known in Japan in the 1950s, c.f. Nobuo Yoneda's (米田信夫) work.


2. Why -手? It seems to be the same agentive morpheme -手 as in 運転手、歌手、選手 etc., but these are words referring to people. Moreover (to my knowledge) -手 is not as productive as, say, -者. Either way, it seems unnatural to calque -or like this.

To ward off any confusion, I do not mean 関手 as in せきて.