sheafificationCompPullback — Mathlib

English

The category SheafOfModules R has limits of all sizes.

Русский

Категория SheafOfModules R имеет пределы во всех размерах.

LaTeX

$$$\operatorname{HasLimitsOfSize}(\mathrm{SheafOfModules}\;R)$$$

Lean4

/-- The pullback of (pre)sheaves of modules commutes with the sheafification. -/
noncomputable def sheafificationCompPullback :
    PresheafOfModules.sheafification (𝟙 S.val) ⋙ pullback.{v} φ ≅
      PresheafOfModules.pullback.{v} φ.val ⋙ PresheafOfModules.sheafification (𝟙 R.val) :=
  Adjunction.leftAdjointUniq
    ((PresheafOfModules.sheafificationAdjunction (𝟙 S.val)).comp (pullbackPushforwardAdjunction φ))
    ((PresheafOfModules.pullbackPushforwardAdjunction φ.val).comp
      (PresheafOfModules.sheafificationAdjunction (𝟙 R.val)))

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