rightDerived_fac_app — Mathlib

English

For any τ: F → F', the rightDerivedDesc interacts compatibly with app components: α.app X ≫ (rightDerivedDesc RF RF' α α' W τ).app (L.obj X) = τ.app X ≫ α'.app X.

Русский

Для любого т: F → F' правыйDerivedDesc согласуется по компонентам на приложениях: ...

LaTeX

$$[τ: F → F'] : α.app X ≫ (RF.rightDerivedDesc α W G β).app (L.obj X) = β.app X$$

Lean4

@[reassoc (attr := simp)]
theorem rightDerived_fac_app (G : D ⥤ H) (β : F ⟶ L ⋙ G) (X : C) :
    α.app X ≫ (RF.rightDerivedDesc α W G β).app (L.obj X) = β.app X :=
  have := IsRightDerivedFunctor.isLeftKanExtension RF α W
  RF.descOfIsLeftKanExtension_fac_app α G β X

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