iso_inv_ι — Mathlib

English

If C is small finitely cocomplete and IsFiltered (CostructuredArrow yoneda A), then PreservesFiniteLimits A.

Русский

Если C малая конечнокомплектная и IsFiltered (CostructuredArrow yoneda A), то PreservesFiniteLimits A.

LaTeX

$$$[IsFiltered(\mathrm{CostructuredArrow}(\mathrm{yoneda}, A))] \Rightarrow \operatorname{PreservesFiniteLimits}(A)$$$

Lean4

@[reassoc (attr := simp)]
theorem iso_inv_ι : (PreservesImage.iso F f).inv ≫ F.map (Abelian.image.ι f) = Abelian.image.ι (F.map f) := by
  simp [iso]

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