20/04/19 17:18:56 ijGx7lvx.net
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[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