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594(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/25(日)09:23 ID:eIdDsFH8(3/19) AAS
>>593
つづき

§ 2.10. Inter-universality: changes of universe as changes of coordinates
One fundamental aspect of the links [cf. the discussion of §2.7, (i)] − namely, the
Θ-link and log-link − that occur in inter-universal Teichm¨uller theory is their incompatibility with the ring structures of the rings and schemes that appear in their
domains and codomains. In particular, when one considers the result of transporting
an ´etale-like structure such as a Galois group [or ´etale fundamental group] across such
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595(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/25(日)09:23 ID:eIdDsFH8(4/19) AAS
>>594
つづき

In this context, we remark that it is also this state of affairs that gave rise to the term
“inter-universal”: That is to say, the notion of a “universe”, as well as the use of
multiple universes within the discussion of a single set-up in arithmetic geometry, already
occurs in the mathematics of the 1960’s, i.e., in the mathematics of Galois categories
and ´etale topoi associated to schemes. On the other hand, in this mathematics of the
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