lower_iso — Mathlib

English

A ternary version of lowering maps a triad of MonoOver into Subobject structure.

Русский

Трёхместная версия понижения отображает тройку MonoOver в структуру Subobject.

LaTeX

$$$\text{lower}_2 F : \text{Subobject } X \to \text{Subobject } Y \to \text{Subobject } Z$$$

Lean4

/-- Isomorphic functors become equal when lowered to `Subobject`.
(It's not as evil as usual to talk about equality between functors
because the categories are thin and skeletal.) -/
theorem lower_iso (F₁ F₂ : MonoOver X ⥤ MonoOver Y) (h : F₁ ≅ F₂) : lower F₁ = lower F₂ :=
  ThinSkeleton.map_iso_eq h

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