W_isInvertedBy_whiskeringRight_presheafToSheaf

English

The W-structure is inverted by whiskering on the right with plusPlusAdjunction, after applying presheafToSheaf.

Русский

Структура W инвертируется правым whiskering через plusPlusAdjunction после presheafToSheaf.

LaTeX

$$$J.W.IsInvertedBy\;((\text{whiskeringRight}_{C^{op}}\; A\; B).obj F) \circ (\text{presheafToSheaf } J B)$$$

Lean4

theorem W_isInvertedBy_whiskeringRight_presheafToSheaf :
    J.W.IsInvertedBy (((whiskeringRight Cᵒᵖ A B).obj F) ⋙ presheafToSheaf J B) :=
  by
  intro P₁ P₂ f hf
  dsimp
  rw [← W_iff]
  exact J.W_of_preservesSheafification F _ hf

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