>>293
おつです。https://twitter.com/math_jin からですね
https://thehighergeometer.wordpress.com/2021/08/06/when-not-to-say-universe/
theHigherGeometer
When not to say “universe”AUGUST 6, 2021 ~ DAVID ROBERTS
(抜粋)
(This post offers no new insights into IUT, it is just an exploration of some of the terminology that gets thrown around. But I had reason to get these ideas down, which I will share later)

Inter-Universal Teichmuller Theory (IUT) is somewhat infamous, to say the least. I want to write about some purely cosmetic thoughts I had recently in a discussion around the use of the term “universe” in IUT. It was curious, because I was, while talking, thinking of the technical term universe i.e. Grothendieck universe and the person that I was talking to had gotten details from a source much closer to the horse’s mouth, and they had the mental image closer to what it apparently really means?and it was not a Grothendieck universe.

However, there seem to be two distinct uses of the term “universe” by Mochizuki. One is the technical sense, given in IUT4 section 3, and explicitly said to be related to size issues and needing to “go up a universe”, as we say, since certain large constructions turn out to stay inside a given Grothendieck universe. I shall always say “Grothendieck universe” for this sense.
略

So here we see again the invocation of the work of Grothendieck and collaborators (this time, no scare quotes), except “universe” here is not the technical sense, but in a more colloquial sense that a (Grothendieck) topos?or more specifically a Galois category, a special case?is a category with rich enough structure that one can work entirely inside it as if it were the whole mathematical universe. This is nicely encapsulated by a cartoon that Ingo Blechschmidt uses to illustrate some of his work:

https://raw.githubusercontent.com/iblech/internal-methods/master/images/external-internal-small.png

つづく
https://twitter.com/5chan_nel (5ch newer account)