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II.2.5_errata

1/27/2022



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Well, that didn't turn out so well, hahahahahaha. Yes, I got slightly overconfident there and genuinely thought I could solve it in time, and ended up embarassing myself. Traumatic. Ahh, yes, I can still hear the Jeopardy music. (cue the part at 2:58 when I wrote "OKAY. I GOT IT.").

Well, I did figure it out later that night... although I'm posting this like 3 days late because I got lazy. Woops. And thus, we are at the VERY FIRST ERRATA OF HARTSHORNED II. WOOOOOOOO *CLAP CLAP CLAP CLAP CLAP*. It ain't Hartshorned without some good old fashioned errata posts. Remember those?


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"WTF"

Anyway, since I already framed the problem in the last post, I can just pick up from there. That's right; the errata motto: IF YOU DROP THE BALL, PICK IT BACK UP. Here's how the story goes. We can actually use initiality of Z again!!! there's a unique morphism.

Z OX(U V )

 
And hence if you localize, the induced local morphisms

ϕP* : Z ϕ(P) AP
ψP* : Z ψ(P) BP

 
are unique. so that Zϕ(P) Zψ(P) = ⇒ϕ(P) = ψ(P). DONE.



"...It took you 3 days to upload that?"



Well, excuuuuuse me princess reader. I'll (try to) upload a post everyday this weekend to make up for it: FRIDAY, SATURDAY, SUNDAY. Are ya happy now, chump? Ready to get your head BASHED with Hartshorned this weekend? Prepare your brain for some very fancy ero guro.

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