現代数学の系譜工学物理雑談古典ガロア理論も読む80

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170(1): 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 11:15:23.61 ID:1QCooAdl(1/7) AAS
>>139
>思うにＲＩＭＳの方針はハッキリしていると思う
> 2020年の４本のワークショップで決着させよう
>「関係者の方、しっかり頑張って、決着させて下さいね」ということでしょう

まあ、大人の事情がある、RIMSをマネージメントする側には
それは、RIMSの経営者としては、避けたい
（「根も葉もない」かもしれないが、風評被害みたいなことね）

多分、2020年に４本のワークショップで、決着させましょうと案画した人がいる
（RIMSの経営層に近い部分でしょう）
ぐだぐだ言わないで、2020年に４本のワークショップを成功させて、しっかり決着させる
それに向けて、全力で、万全の準備をすべきと思います

「黒幕」とか、おらんでしょう
健全な経営判断と思います
「ブラックホール状態」というけれど、４本のワークショップというチャンスは与えられている
そのチャンスを生かすべき

（参考）
新一の「心の一票」 - 楽天ブログ https://plaza（ >>16 or URLがNGなので、キーワードでググれ（＾＾）
2020.01.05
宇宙際タイヒミューラー理論（IUTeich）の論文を巡る現状報告：「数学界に出現している悲惨なブラックホールの物語」
(抜粋)
ここで一つ注意しなければならない点ですが、この（本来優先されるべき「学問の健全な発展」という観点からして）余りにも奇妙で非建設的な「ブラックホール状態」の糸を引いている「黒幕」の正体については私は全く情報を持っておりません。
つまり、「ブラックホール状態」の発生が、雑誌の関係者の独自の判断によるものなのか、海外の有力者の（何等かの人脈を介した）直接的な圧力によるものなのか、海外の「激しい敵意」に対して文科省官僚や大学の行政関係者が「忖度」をして雑誌に掛けた圧力によるものなのか、無数の可能性が頭が浮かびますが、現時点ではその発生の仕組みの解明には至っておりません。
別の言い方をすれば、本記事の冒頭で「一種の内部告発」という表現を用いましたが、その広い意味での告発の対象は「海外の数学界のとある勢力による無意味な数学的な誤解」ということになりますが、より直接的・具体的な意味での告発の対象である「非建設的なブラックホールを発生させている黒幕」の正体は不詳のままであるということになります。

171(1): 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 11:27:25.70 ID:1QCooAdl(2/7) AAS
>>170 追加

”the emphasis on the types ("species") of objects”（下記）って、なんですかね？
あんまし、説得力ないと思う
それより、圏論的説明をしっかりやるべきでは？（＾＾；
（"species"って、マイナーな印象しか受けない。数学のメインストリームじゃないでしょ？）

https://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCller_theory
Inter-universal Teichmuller theory
(抜粋)
History
In March 2018, Peter Scholze and Jakob Stix visited Kyoto University for five days of discussions with Mochizuki and Yuichiro Hoshi; while this did not resolve the differences, it brought into focus where the difficulties lay.[8][10]

In September 2018, Mochizuki wrote a 41-page summary of his view of the discussions and his conclusions about which aspects of his theory he considers misunderstood.[12] In particular he names:
・"re-initialization" of (mathematical) objects, making their previous "history" inaccessible;
・"labels" for different "versions" of objects;
・the emphasis on the types ("species") of objects.

Google訳
2018年9月、望月は彼の議論の見解と彼の理論のどの側面が誤解されていると考えるかについての結論の41ページの要約を書いた。[12]特に彼は次のように名前を付けています。
・（数学）オブジェクトの「再初期化」。以前の「履歴」にアクセスできなくなります。
・オブジェクトのさまざまな「バージョン」の「ラベル」。
・オブジェクトのタイプ（「種」）の強調。

173(1): 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 11:58:02.25 ID:1QCooAdl(3/7) AAS
>>171 追加

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
IUTそのIV
(抜粋)
P68
In the following discussion, we use the phrase “set-theoretic formula” as it is
conventionally used in discussions of axiomatic set theory [cf., e.g., [Drk], Chapter 1,
§2], with the following proviso: In the following discussion, it should be understood
that every set-theoretic formula that appears is “absolute” in the sense that its
validity for a collection of sets contained in some universe V relative to the model
of set theory determined by V is equivalent, for any universe W such that V ∈ W,
to its validity for the same collection of sets relative to the model of set theory
determined by W [cf., e.g., [Drk], Chapter 3, Definition 4.2].
Definition 3.1.
(i) A 0-species S0 is a collection of conditions given by a set-theoretic formula
P85
Bibliography
[Drk] F. R. Drake, Set Theory: an Introduction to Large Cardinals, Studies in Logic
and the Foundations of Mathematics 76, North-Holland (1974).

https://www.researchgate.net/publication/270260913_Drake_Frank_R_Set_theory_An_introduction_to_large_cardinals_Studies_in_logic_and_the_foundations_of_mathematics_vol_76_North-Holland_Publishing_Company_Amsterdam_and_London_and_American_Elsevier_Publi
researchgate
Drake Frank R.. Set theory. An introduction to large cardinals. Studies in logic and the foundations of mathematics, vol. 76. North-Holland Publishing Company, Amsterdam and London, and American Elsevier Publishing Company, Inc., New York, 1974, xii + 351 pp.

174: 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 11:59:01.50 ID:1QCooAdl(4/7) AAS
>>172
同意です（＾＾；

175(3): 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 12:09:40.94 ID:1QCooAdl(5/7) AAS
>>173 追加

species って、nLabでは圏論なんだけど
望月 IUT4 §3では、ZFCの集合論みたく書いてある
はてはて？（＾＾；

https://ncatlab.org/nlab/show/species
nLab
species
(抜粋)
1. Idea
A (combinatorial) species is a presheaf or higher categorical presheaf on the groupoid core(FinSet), the permutation groupoid.

A species is a symmetric sequence by another name. Meaning: they are categorically equivalent notions.

2. Definition
1-categorical

2-categorical

(∞,1) -categorical

Operations on species
There are in fact 5 important monoidal structures on the category of species.

176(1): 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 12:15:31.15 ID:1QCooAdl(6/7) AAS
>>175 追加

IUTその4に下記説明ある
が、圏論で筋通した方が良さそう？

P72
Example 3.2. Categories. The notions of a [small] category and an isomorphism class of [covariant] functors between two given [small] categories yield an
example of a species. That is to say, at a set-theoretic level, one may think of a
[small] category as, for instance, a set of arrows, together with a set of composition
relations, that satisfies certain properties; one may think of a [covariant] functor
between [small] categories as the set given by the graph of the map on arrows determined by the functor [which satisfies certain properties]; one may think of an
isomorphism class of functors as a collection of such graphs, i.e., the graphs determined by the functors in the isomorphism class, which satisfies certain properties.
Then one has “dictionaries”
0-species ←→ the notion of a category
1-species ←→ the notion of an isomorphism class of functors
at the level of notions and
a 0-specimen ←→ a particular [small] category
a 1-specimen ←→ a particular isomorphism class of functors
at the level of specific mathematical objects in a specific ZFC-model. Moreover, one
verifies easily that species-isomorphisms between 0-species correspond to isomorphism classes of equivalences of categories in the usual sense.

Remark 3.2.1. Note that in the case of Example 3.2, one could also define a
notion of “2-species”, “2-specimens”, etc., via the notion of an “isomorphism of
functors”, and then take the 1-species under consideration to be the notion of a
functor [i.e., not an isomorphism class of functors]. Indeed, more generally, one
could define a notion of “n-species” for arbitrary integers n ? 1. Since, however,
this approach would only serve to add an unnecessary level of complexity to the
theory, we choose here to take the approach of working with “functors considered up to isomorphism”.

177(1): 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE [] 2020/01/08(水) 19:04:57.09 ID:1QCooAdl(7/7) AAS
>>175 追加
species って、wikipedia では、下記 Combinatorial species なのだが、望月先生と同じ意味か？
Andre Joyal 抜きには語れないようだが、望月 IUT4には Joyal先生の名前が出てこない（＾＾；

https://en.wikipedia.org/wiki/Combinatorial_species
Combinatorial species
(抜粋)
In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions.
Examples of discrete structures are (finite) graphs, permutations, trees, and so on; each of these has an associated generating function which counts how many structures there are of a certain size.
One goal of species theory is to be able to analyse complicated structures by describing them in terms of transformations and combinations of simpler structures.

https://en.wikipedia.org/wiki/Andr%C3%A9_Joyal
(抜粋)
Andre Joyal (born 1943) is a professor of mathematics at the Universite du Quebec a Montreal who works on category theory. He was a member of the School of Mathematics at the Institute for Advanced Study in 2013,[1] where he was invited to join the Special Year on Univalent Foundations of Mathematics.[2]

Research
He discovered Kripke?Joyal semantics,[3] the theory of combinatorial species and with Myles Tierney a generalization of the Galois theory of Alexander Grothendieck[4] in the setup of locales. Most of his research is in some way related to category theory, higher category theory and their applications.
He did some work on quasi-categories, after their invention by Michael Boardman and Rainer Vogt, in particular conjecturing[5] and proving the existence of a Quillen model structure on sSet whose weak equivalences generalize both equivalence of categories and Kan equivalence of spaces.
He co-authored the book "Algebraic Set Theory" with Ieke Moerdijk and recently started a web-based expositional project Joyal's CatLab [6] on categorical mathematics.

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