quasiIsoAt_extendMap_iff — Mathlib

English

For any φ and i, QuasiIsoAt (extendMap φ e) i is equivalent to QuasiIsoAt φ i, given appropriate homology data.

Русский

Для любого φ и i, QuasiIsoAt (extendMap φ e) i эквивалентно QuasiIsoAt φ i при наличии соответствующих данных гомологий.

LaTeX

$$QuasiIsoAt (extendMap φ e) i' ↔ QuasiIsoAt φ i$$

Lean4

theorem quasiIsoAt_extendMap_iff : QuasiIsoAt (extendMap φ e) j' ↔ QuasiIsoAt φ j :=
  by
  simp only [quasiIsoAt_iff_isIso_homologyMap]
  exact
    (MorphismProperty.isomorphisms C).arrow_mk_iso_iff
      (Arrow.isoMk (K.extendHomologyIso e hj') (L.extendHomologyIso e hj'))

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