>>538 補足
>いまどきの普通の圏論の教科書を読んだ人が
>”宇宙”とか言われると
>違和感あると思うな

下記のベーシック圏論 Leinsterに、”宇宙”が2箇所出てくる

https://www.maruzen-publishing.co.jp/item/?book_no=295027
ベーシック圏論 普遍性からの速習コース
原書名 Basic Category Theory
著者名 斎藤　恭司 監修 土岡　俊介 訳 丸善出版 2017年01月
＜arxiv公開＞
https://arxiv.org/abs/1612.09375
Basic Category Theory Tom Leinster
[v1] Fri, 30 Dec 2016 03:02:01 UTC (210 KB)
Journal reference: Cambridge Studies in Advanced Mathematics, Vol. 143, Cambridge University Press, 2014
Download:PDF https://arxiv.org/pdf/1612.09375

P2 （圏論の‘universal’の説明で、the universe of sets と使っている）
Properties such as this are called ‘universal’ because they state how the object being described (in this case, the set 1) relates to the entire universe in which it lives (in this case, the universe of sets).
The property begins with the words ‘for all sets X’, and therefore says something about the relationship
between 1 and every set X: namely, that there is a unique map from X to 1.

つづく