mapRightHomologyIso_eq — Mathlib

English

The morphism h.i is mono: every pair of arrows f,g with f ≫ h.i = g ≫ h.i must satisfy f = g.

Русский

Морфизм h.i мономорфизм: любые два стертых на h.i стрелы равны, если их прерывания совпадают.

LaTeX

$$$\operatorname{Mono}(h.i)$$$

Lean4

theorem mapRightHomologyIso_eq [S.HasRightHomology] [F.PreservesRightHomologyOf S] :
    S.mapRightHomologyIso F = (hr.map F).rightHomologyIso ≪≫ F.mapIso hr.rightHomologyIso.symm :=
  by
  ext
  dsimp [mapRightHomologyIso, rightHomologyIso]
  simp only [map_rightHomologyMap', ← rightHomologyMap'_comp, Functor.map_id, comp_id, Functor.mapShortComplex_obj]

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