epi_homologyMap_of_epi_of_not_rel

English

A variant of the inverse-hom-id relation for isoHomologyπ in a different indexing setup.

Русский

Вариант равенства обратного к Homology-пу для isoHomologyπ в другой нумерации.

LaTeX

$$$$ (isoHomologyπ i j hi h)^{-1} \circ homologyπ_j = \mathrm{Id} $$$$

Lean4

theorem epi_homologyMap_of_epi_of_not_rel (φ : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i] [Epi (φ.f i)]
    (hi : ∀ j, ¬c.Rel i j) : Epi (homologyMap φ i) :=
  ((MorphismProperty.epimorphisms C).arrow_mk_iso_iff
        (Arrow.isoMk (K.isoHomologyι i _ rfl (shape _ _ _ (by tauto)))
          (L.isoHomologyι i _ rfl (shape _ _ _ (by tauto))))).2
    (MorphismProperty.epimorphisms.infer_property (opcyclesMap φ i))

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