leftDerived_fac_app — Mathlib

English

The fac-app relation for leftDerived lifts asserts that (LF.leftDerivedLift α W G β).app (L.obj X) composed with α.app X equals β.app X.

Русский

Утверждение fac-app для левого производного отображает, что (LF.leftDerivedLift α W G β).app (L.obj X) затем α.app X равно β.app X.

LaTeX

$$$$ (LF.leftDerivedLift α W G β).app (L.obj X) \circ α.app X = β.app X. $$$$

Lean4

@[reassoc (attr := simp)]
theorem leftDerived_fac_app (G : D ⥤ H) (β : L ⋙ G ⟶ F) (X : C) :
    (LF.leftDerivedLift α W G β).app (L.obj X) ≫ α.app X = β.app X :=
  have := IsLeftDerivedFunctor.isRightKanExtension LF α W
  LF.liftOfIsRightKanExtension_fac_app α G β X

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