Inter-universal geometry と ABC予想 (応援スレ) 44

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 44 (1002ﾚｽ)
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62: １３２人目の素数さん [sage] 2020/04/14(火) 13:35:10 ID:PFls8jJA

>>61

つづき

Or that you incorrectly calculate the perfection of a ring if in the usual sequential colimit you don’t create separate copies of the ring in advance (this is LbEx3). This is patently absurd, but makes sense if one assumes that diagrams *must* be injective functors, or rather, literal subcategories.
Recall that M assumes that he is identifying isomorphic functors, so that the concept of a diagram qua functor is severely underdetermined.
Working up to isomorphism like this, and replacing a diagram with one that produces an isomorphic (co)limit, one can safely assume that diagrams are subcategories?but it is super weird, and it took me ages to realise that was what he was thinking.
This is why he talks about things like “forgetting histories”, because he is thinking that you need to somehow create fresh, distinct copies of objects in order to not collapse the subcategory down, and thereby give a different diagram.
So when someone versed in standard category-theoretic language says “let’s identify these objects”, he seems to hear it as “let’s collapse this subcategory to something trivial”.
And when he says “I need distinct copies”, it seems totally weird and unmotivated. So when I look at LbEx3 in the 2018 Report it looks like the sort of mistake a student would make, when learning category theory for the first time.
The problem is his conceptions of basic notions seem to be so idiosyncratic that without a serious translation filter, what he is saying seems to be completely off the wall.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1586655469/62

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