[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 76 (1002ﾚｽ)
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810(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 10/28(火)17:39 ID:wRqXRloP(7/9) AAS
>>808
(引用開始)
Localization of categories
This procedure, however, in general yields a proper class of morphisms between X and Y.
Typically, the morphisms in a category are only allowed to form a set. Some authors simply ignore such set-theoretic issues.

Model categories
A rigorous construction of localization of categories, avoiding these set-theoretic issues, was one of the initial reasons for the development of the theory of model categories: a model category M is a category in which there are three classes of maps; one of these classes is the class of weak equivalences.
The homotopy category Ho(M) is then the localization with respect to the weak equivalences.
The axioms of a model category ensure that this localization can be defined without set-theoretical difficulties.

Examples
省18

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811(3): 現代数学の系譜 雑談 ◆yH25M02vWFhP 10/28(火)17:48 ID:wRqXRloP(8/9) AAS
>>810
さらに要約する
Localization of categories で 下記問題が生じる
”This procedure, however, in general yields a proper class of morphisms between X and Y.
Typically, the morphisms in a category are only allowed to form a set. Some authors simply ignore such set-theoretic issues.”

その解決法の一つが
Model categories らしい

関連 Related concepts で
Bousfield localization of a model category があるらしく
Ohkawa の定理 は、ここで働いて proper class→ 集合 に 落とせる（>>783 信州大 より）
省1

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814: 10/28(火)20:23 ID:TjJPW5+0(3/5) AAS
>>810
＞要するに・・・が、肝らしい

要するにバカラスは何一つ理解できず理解不能語の海で溺死した、と

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