[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 45 (1002ﾚｽ)
上下前次1-新
抽出解除 ﾚｽ栞
このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ
500(4): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/05/11(月)17:39 ID:zmgc47N7(15/17) AAS
>>499
つづき
(ii) In the context of constructing “loops” in a mutation-history as in the final display of (i), we observe that the simpler the structure of the species involved, the easier it is to construct “loops”.
It is for this reason that species such as the species determined by the notion of a category [cf. Example 3.2] are easier to work with, from the point of view of
constructing “loops”, than more complicated species such as the species determined by the notion of a scheme. This is one of the principal motivations for the “geometry of categories”
- of which “absolute anabelian geometry” is the special case that arises when the categories involved are Galois categories
- i.e., for the theory of representing scheme-theoretic geometries via categories [cf., e.g., the Introductions of [MnLg], [SemiAnbd], [Cusp], [FrdI]].
省4
117(1): IUT応援団 団員 2020/05/05(火)18:19 ID:zuve741i(8/13) AAS
>>107
>いいんじゃね？
>勝手でしょ
>放し飼いで
では、入部ということで
押忍！
>>115
省5
501(2): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/05/11(月)17:39 ID:zmgc47N7(16/17) AAS
>>500
つづき
(iii) Again in the context of mutation-histories such as the one given in the final display of (i), although one may, on certain occasions, wish to apply various
mutations that fundamentally alter the structure of the mathematical objects involved and hence give rise to “output species-objects” of the “S” on the right that
are related in a highly nontrivial fashion to the “input species-objects” of the “S”on the left, it is also of interest to consider
“portions” of the various mathematical objects that occur that are left unaltered by the various mutations that one applies.
This is precisely the reason for the introduction of the notion of a core of a mutationhistory. One important consequence of the construction of various cores associated to a mutation-history is that often
省6
504: IUT応援団 団員 2020/05/11(月)18:08 ID:zRqOWOEd(14/15) AAS
>>498-501
これだってただ漫然と貼っただけで絶対読んでないでしょ
読んだって意味わからないでしょ 数学全般素人の団長には
507(1): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/05/11(月)20:03 ID:AHfZgdJQ(6/15) AAS
>>498-501 補足
このIUT IV P74 Remark 3.3.1. をコピーしたのは
“∈-loops”とか、”∈-structure of the set theory”とか ”In the context of constructing “loops” in a mutation-history”、”“output species-objects” of the “S” on the right that”
とか
なんか (>>463より) 渕野 「基礎の公理」
”基礎の公理は技術的な理由で付け加えられた公理と言えるが，
この公理を集合論の公理系に加えることの妥当性は，
省11
上下前次1-新書関写板覧索設栞歴
ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ
ぬこの手 ぬこTOP 0.035s