[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 50 (1002ﾚｽ)

Inter-universal geometry と ABC予想 50 http://rio2016.5ch.net/test/read.cgi/math/1586907848/

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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 t

he 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

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