I should've added that in the internal logic / type theory of any topos FunExt always holds.
So, my thread below in fact proves that the following categories are not topoi:
- Poly(C), for any category C with pullbacks
- Game Categories
- The syntactic category of TTs
naively, functional extensionality (funext) says if two functions take equal values, then they are equal.
Two observations about funext:
1. If you're new to type theory, it's instructive to think about why funext fails in the initial/syntactic model – don't cheat with ai!
In France, Uber couriers are manipulating the delivery system: by collectively refusing to accept low-paying orders, they are forcing the delivery companies’ algorithms to increase payments.
As automated hacking starts to take off, AI company employees are saying that now is a good time to start recording audio logs to leave scattered around
In one day, two politicians - Bolsonaro in Brazil and Vucic in Serbia - with ties to Trump and his family have lost surprise elections, thanks to high turnout. The rise of the international far-right is not inevitable.
A good documentary telling the story of Israel-Iran recent wars from Iranian pov since 1 April 2024 when Israel conducted airstrike on the Iranian embassy complex in Damascus, Syria.
https://t.co/pu8yJuDarK
@FahadHandle@policytensor recall what Khomeini did with Carter, even though he came to an agreement in the Algiers Accords, the actual physical release of the hostages was delayed until minutes after Reagan concluded his inaugural address. Something similar maybe?
@MartinPerring@MacaesBruno "historical progress" is not unique to enlightenment, soviet communism had it in abundance, in fact even more intensely. One of the core values of enlightenment is that the government derives its limited power from the consent of the governed, with checks and balances.
@mroocows@47Tolkien@grok purchase is not "propping up", China needs that oil, esp. with that discount premium. it's out of self interest not assistance.
@mroocows@47Tolkien "propping Iran's economy" you say?!
@grok
how much has China invested in Iran in total in the past several years? also, compare that to China's investment in KSA.
UK HS2:
> Proposed in 2010
> Phase 1 was expected to open by Dec 2026
> As of May 2026, passenger services are not expected to begin before 2036.
all it achieved: destruction of 32 hectares of ancient woodland for Phase 1 alone. More to fell. No passenger until 2036!