cechConerveAdjunction — Mathlib

English

A proof component for the equivalence between Čech conerve morphisms and arrow morphisms, detailing the isomorphism properties.

Русский

Часть доказательства эквиваленции между морфизмами Čech-конвервы и стрелки, описывающая изоморфизмы.

LaTeX

$$$\\text{cechConerveEquiv} \\;\\text{is an equivalence of Hom-sets: } (F.augmentedCechConerve \\to X) \\cong (F \\to Augmented.toArrow.obj X).$$$

Lean4

/-- The augmented Čech conerve construction is left adjoint to the `toArrow` functor. -/
abbrev cechConerveAdjunction : augmentedCechConerve ⊣ (Augmented.toArrow : _ ⥤ Arrow C) :=
  Adjunction.mkOfHomEquiv { homEquiv := cechConerveEquiv }

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