lowerAdjunction — Mathlib

English

A general adjunction between MonoOver categories induces an adjunction between Subobject categories after lowering.

Русский

Общая adjunction между категориями MonoOver индуцирует adjunction между Subobject через понижение.

LaTeX

$$$\text{lowerAdjunction } L R : \text{lower } L \dashv \text{lower } R$$$

Lean4

/-- An adjunction between `MonoOver A` and `MonoOver B` gives an adjunction
between `Subobject A` and `Subobject B`. -/
def lowerAdjunction {A : C} {B : D} {L : MonoOver A ⥤ MonoOver B} {R : MonoOver B ⥤ MonoOver A} (h : L ⊣ R) :
    lower L ⊣ lower R :=
  ThinSkeleton.lowerAdjunction _ _ h

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