Inter-universal geometry と ABC予想 50

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 50 (1002ﾚｽ)
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691: 現代数学の系譜 雑談 ◆e.a0E5TtKE  [sage] 2020/04/19(日) 17:18:56.59 ID:ijGx7lvx

>>690 追加
つづき

また下記
[Note that this terminology differs from the standard terminology of category theory, but will be natural in the context of the theory of the present series of papers.]
[なお、この用語はカテゴリー理論の標準用語とは異なるが、今回の一連の論文の理論の文脈では当然のことであろう]
まあ、こういうところ、「独善」と紙一重だろうね〜（OP氏がいうのはこういうところかも） ｗ（＾＾；

なお、
”an “isomorphism C→D” is precisely an “isomorphism in the usual sense”of the [1-]category constituted by the coarsification of the 2-category of all small 1-categories relative to a suitable universe with respect to which C and D are small.”
で
「relative to a suitable universe」も、当初の”universe”定義による用語の使い方として、整合しているのかどうかだね〜？（＾＾；
（先のは、集合論の”universes associated to the distinct fiber functors/basepoints on either side of such a non-ring/scheme-theoretic filter”だったのにね。まあ、重箱の隅とは思うが ）

P33
Section 0: Notations and Conventions
Monoids and Categories:

We shall refer to an isomorphic copy of some object as an isomorph of the object.
If C and D are categories, then we shall refer to as an isomorphism C→D any isomorphism class of equivalences of categories C→D.
[Note that this terminology differs from the standard terminology of category theory, but will be natural in the context of the theory of the present series of papers.]
Thus, from the point of view of “coarsifications of 2-categories of 1-categories”
[cf. [FrdI], Appendix, Definition A.1, (ii)],
an “isomorphism C→D” is precisely an “isomorphism in the usual sense”of the [1-]category constituted by the coarsification of the 2-category of all small 1-categories relative to a suitable universe with respect to which C and D are small.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1586907848/691

759: 現代数学の系譜 雑談 ◆e.a0E5TtKE  [sage] 2020/04/20(月) 07:50:35.74 ID:w4pNIZe5

>>757 補足
>そもそも、”同型”なる用語の意味が、数学用語としては、その文脈毎に異なることは、常識（当たり前）だろう
>（余談だが 望月論文も、それを言っているとおもうが、確かに分かり難いと思った）

下記の望月ＩＵＴ Ｉ Ｐ39の ”isomorphism”およびＮｏｔｅの記述
[Note that this terminology differs from the standard terminology of category theory, but will be natural in the context of the theory of the present series of papers.]
なら、i-isomorphism とかのネーミングにすれば良かった気がする
（i-isomorphismって、i-phone みたいで 格好いいだろ？ｗ（＾＾；　）

>>691より
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf
INTER-UNIVERSAL TEICHMULLER THEORY I: CONSTRUCTION OF HODGE THEATERS Shinichi Mochizuki April 2020
(抜粋)
P33
Section 0: Notations and Conventions
Monoids and Categories:

http://rio2016.5ch.net/test/read.cgi/math/1586907848/759

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