sheafificationAdjunction_homEquiv_apply

English

The application of the homEquiv under the adjunction to a morphism f is equal to the standard sheafification homEquiv evaluation.

Русский

Применение гомоэквивалентности под адъункцией к отображению f равно обычной оценке гомэквивалентности шейификации.

LaTeX

$$$ (sheafificationAdjunction \alpha).homEquiv P F f = sheafificationHomEquiv \alpha f $$$

Lean4

theorem sheafificationAdjunction_homEquiv_apply {P : PresheafOfModules.{v} R₀} {F : SheafOfModules.{v} R}
    (f : (sheafification α).obj P ⟶ F) : (sheafificationAdjunction α).homEquiv P F f = sheafificationHomEquiv α f :=
  rfl

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