toSheafify_naturality — Mathlib

English

A particular equality between piComparison and forkMap holds, after unfolding forkMap and using the coproduct–product isomorphism.

Русский

Утверждается равенство между piComparison и forkMap после раскрытия forkMap и использования изоморфности копроизвестие–произведение.

LaTeX

$$$\text{piComparison}_F = F.map(\mathrm{opCoproductIsoProduct}'\,hc\,\mathrm{(productIsProduct }\_\text{)} ).inv \circ Equalizer.Presieve.Arrows.forkMap F X c.inj$$$

Lean4

@[reassoc (attr := simp)]
theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : η ≫ toSheafify J _ = toSheafify J _ ≫ sheafifyMap J η :=
  sheafificationAdjunction J D |>.unit.naturality η

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