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Inter-universal geometry と ABC予想 (応援スレ) 49

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>>554
> >>553
> 
> つづき
> 
> Ｐ50
> (i) Types of mathematical objects: In the following discussion, we shall often
> speak of “types of mathematical objects”, i.e., such as groups, rings, topological
> spaces equipped with some additional structure, schemes, etc. This notion of a “type
> of mathematical object” is formalized in [IUTchIV], §3, by introducing the notion of
> a “species”. On the other hand, the details of this formalization are not so important
> for the following discussion of the notion of multiradiality. A “type of mathematical
> object” determines an associated category consisting of mathematical objects of this
> type ? i.e., in a given universe, or model of set theory ? and morphisms between such
> mathematical objects. On the other hand, in general, the structure of this associated
> category [i.e., as an abstract category!] contains considerably less information than the
> information that determines the “type of mathematical object” that one started with.
> For instance, if p is a prime number, then the “type of mathematical object” given by
> rings isomorphic to Z/pZ [and ring homomorphisms] yields a category whose equivalence
> class as an abstract category is manifestly independent of the prime number p.
> 
> つづく

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