map_rightHomologyMap' — Mathlib

English

For S1, S2 with right homology data, naturality of opcyclesMap under F: F.map (ShortComplex.opcyclesMap' φ hr1 hr2) = ShortComplex.opcyclesMap' (F.mapShortComplex.map φ) (hr1.map F) (hr2.map F).

Русский

Для S1, S2 с данными правой гомологии натуральность opcyclesMap под F: F.map (ShortComplex.opcyclesMap' φ ...) = ShortComplex.opcyclesMap' (F.mapShortComplex.map φ) ...

LaTeX

$$$F.map (ShortComplex.opcyclesMap' \phi \ hr_1 \ hr_2) = ShortComplex.opcyclesMap' (F.mapShortComplex.map \phi) (hr_1.map F) (hr_2.map F).$$$

Lean4

theorem map_rightHomologyMap' :
    F.map (ShortComplex.rightHomologyMap' φ hr₁ hr₂) =
      ShortComplex.rightHomologyMap' (F.mapShortComplex.map φ) (hr₁.map F) (hr₂.map F) :=
  by
  have γ : ShortComplex.RightHomologyMapData φ hr₁ hr₂ := default
  rw [γ.rightHomologyMap'_eq, (γ.map F).rightHomologyMap'_eq, ShortComplex.RightHomologyMapData.map_φH]

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