>>375　＞”species”が、大活躍している風では無い。はて？

∧と∨の論文の頁140に、閉じたループはIUTの最後の部分にだけ出てくるとあった。検索したら論文の最後だけで正しいよ。

またそれが [IUTchIV],§3でspeciesを論じた動機とある。

Indeed, it is precisely this aspect of the constructions of inter-universal Teichm¨uller
theory that motivated the author to include the discussion of species in [IUTchIV],
§3.
Finally, we recall — cf. also the discussion of §3.10 [especially, (Stp7)] below
— that
(LVsQ) it is only in the final portion of inter-universal Teichm¨uller theory, i.e.,
once one obtains a formal (sub)quotient that forms a “closed loop”, that
one may pass from this formal (sub)quotient to a “coarse/set-theoretic
(sub)quotient” by taking the log-volume
Indeed, it is precisely this aspect of the constructions of inter-universal Teichm¨uller
theory that motivated the author to include the discussion of species in [IUTchIV],
§3.
Finally, we recall — cf. also the discussion of §3.10 [especially, (Stp7)] below
— that
(LVsQ) it is only in the final portion of inter-universal Teichm¨uller theory, i.e.,
once one obtains a formal (sub)quotient that forms a “closed loop”, that
one may pass from this formal (sub)quotient to a “coarse/set-theoretic
(sub)quotient” by taking the log-volume

"属性方程式a∈aを解きたい”の論文では、頁１に、「種」の概念と、頁２に、代数だと極限の近似しかできないが、一種の解析・極限まで行けば「a∈a」の解が！とあり、また、「ケン／圏の同値」の商を考えるとこのような解析・極限の幾何ができる、との要件があった。

ＩＵＴは、望月の他の研究と同様に（圏/圏の同値）の商を使い、「種」の概念を導入するけれど、それは最後で閉じたループを形成する商があるからか。

あと北大の論文で、Joshi証明戦略で課題にあった、素点が扱えるのか？もスケッチされているね。