Naïm Camille Favier

(homotopy, cubical) type theory, category theory, functional programming, music. PhD student at Chalmers. Any pronouns.
@[email protected]

[Naïm Camille Favier @ncfavier]

@sarah_zrf in french we have the dual version of this: futur antérieur conjectural (using the future perfect to make conjectures about the past)

[Naïm Camille Favier @ncfavier]

@T_Gamard ptdr

[Naïm Camille Favier @ncfavier]

@gro_tsen Just in time before the question was closed! It's pretty strange how poorly received constructive maths questions are on MSE...

[Naïm Camille Favier @ncfavier]

@sarah_zrf @ImpliedFeline *yells at you for being on Twitter*

[Naïm Camille Favier @ncfavier]

@gro_tsen Was Eilenberg also involved in the decision? /j

[Naïm Camille Favier @ncfavier]

@Moinsdeuxcat Je suppose que tu connais cette page https://t.co/YpbBXnouEW

[Naïm Camille Favier @ncfavier]

@CherryshAluna Aviations - Luminaria

https://t.co/P93XrM7kS6

[Naïm Camille Favier @ncfavier]

@gro_tsen Je ne sais pas si tu as vu les travaux d'Andrew Swan sur les modalités d'oracle (au sens monadique): https://t.co/Gjjz5PayJy

[Naïm Camille Favier @ncfavier]

@Moinsdeuxcat @gro_tsen @tejotaefe Indeed, there is only a groupoid of all fields (half-joking)

[Naïm Camille Favier @ncfavier]

@gro_tsen 5 is of the form 4n + 1, so there are primitive Pythagorean triples a² + b² = c² with c = 5ᵐ for every m (says Wikipedia). From one of these we get (2ᵐa/10ᵐ)² + (2ᵐb/10ᵐ)² = 1. It remains to show that we get different points for different values of m...

[Naïm Camille Favier @ncfavier]

@sarah_zrf Yeah I'm not satisfied with this story. The idea is that P is in the image of the pullback functor π* because it's "well-behaved", so if we have colim(P) ≃ X we get P ≃ π*(X). In other words we can use descent for well-behaved things. This feels very roundabout.

[Naïm Camille Favier @ncfavier]

@sarah_zrf As in, Sub(—) is representable so it preserves limits.

[Naïm Camille Favier @ncfavier]

@sarah_zrf I think so; my guess is that since a topos has a subobject classifier all colimits are (-1)-van Kampen, just like all colimits are van Kampen in an ∞-topos because it has object classifiers.

[Naïm Camille Favier @ncfavier]

@sarah_zrf Yeah, the particular delooping I have in mind is the type of 2-element types (so, types merely equivalent to Fin 2). |I| is just the underlying type of I. See https://t.co/nNhNsiLK7U

[Naïm Camille Favier @ncfavier]

@sarah_zrf We get this by universality if we can show that the top diagram is a quotient, which I think is easy enough if P is well-behaved (there's probably a more abstract argument here...).

[Naïm Camille Favier @ncfavier]

@sarah_zrf I think it looks like this: we have a section of ι^* P and we want to get a section of P, so it suffices to prove that the square formed by π is a pullback. /