extendHomologyIso_hom_homologyι — Mathlib

English

A naturality statement for extendHomologyIso with respect to homologyι maps.

Русский

Естественная натуральность extendHomologyIso по отношению к гомологиям homologyι.

LaTeX

$$Theorem: (extendHomologyIso e hj').hom ≫ homologyι j = extend homologyι j' ≫ extendOpcyclesIso... (schematic)$$

Lean4

@[reassoc (attr := simp)]
theorem extendHomologyIso_hom_homologyι :
    (K.extendHomologyIso e hj').hom ≫ K.homologyι j = (K.extend e).homologyι j' ≫ (K.extendOpcyclesIso e hj').hom := by
  simp only [← cancel_epi ((K.extend e).homologyπ j'), homologyπ_extendHomologyIso_hom_assoc, homology_π_ι,
    extendCyclesIso_hom_iCycles_assoc, homology_π_ι_assoc, pOpcycles_extendOpcyclesIso_hom]

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