ε — Mathlib · SciLib

English

Localization interacts compatibly with adjunctions, providing unit and counit formulas for localized functors.

Русский

Локализация совместима с адукциями, обеспечивая формулы единицы и ковечения для локализованных функторов.

LaTeX

$$$\\eta\\_app,\\epsilon\\_app,\\text{ and localization unit/counit relations hold for localized adjunctions.}$$$

Lean4

/-- Auxiliary definition of the unit morphism for the adjunction `Adjunction.localization` -/
noncomputable def ε : 𝟭 D₁ ⟶ G' ⋙ F' :=
  by
  letI : Lifting L₁ W₁ ((G ⋙ F) ⋙ L₁) (G' ⋙ F') := Lifting.mk (CatCommSq.hComp G F L₁ L₂ L₁ G' F').iso.symm
  exact Localization.liftNatTrans L₁ W₁ L₁ ((G ⋙ F) ⋙ L₁) (𝟭 D₁) (G' ⋙ F') (whiskerRight adj.unit L₁)

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