toSheafify_naturality — Mathlib

English

Naturality of the toSheafify construction with respect to composition of morphisms, expressed in a three-arrow equation.

Русский

Естественность конструкций toSheafify по отношению к композициям морфизмов.

LaTeX

$$$\\eta : P \\to Q$ implies (toSheafify P) \\circ (toSheafify Q) = ...$$$

Lean4

@[reassoc (attr := simp)]
theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η :=
  by
  dsimp [sheafifyMap, sheafify, toSheafify]
  simp

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