[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 45 (1002ﾚｽ)
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499(3): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/05/11(月)17:39 ID:zmgc47N7(14/17) AAS
>>498
つづき

In some sense, the notions of a “set” and of a “bijection of sets” allow one to achieve such “identifications”.
That is to say, the mathematical objects at both higher and lower levels of the ∈-structure constitute examples of the same mathematical notion of a “set”,
so that one may consider “bijections of sets” between those sets without violating the axiom of foundation.
In some sense, the notion of a species may be thought of as a natural extension of this observation.
That is to say,
省6

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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

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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

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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

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