truncLE'Map_f_eq_cyclesMap — Mathlib

English

IsIso(K.πTruncGE e) is equivalent to K being strictly supported along e.

Русский

Изоморфизм(K.πTruncGE e) эквивалентен тому, что K строго поддержан вдоль e.

LaTeX

$$$\text{IsIso}\bigl(K.\pi_{\mathrm{TruncGE}}(e)\bigr) \iff K.\mathrm{IsStrictlySupported}(e)$$$

Lean4

theorem truncLE'Map_f_eq_cyclesMap {i : ι} (hi : e.BoundaryLE i) {i' : ι'} (h : e.f i = i') :
    (truncLE'Map φ e).f i = (K.truncLE'XIsoCycles e h hi).hom ≫ cyclesMap φ i' ≫ (L.truncLE'XIsoCycles e h hi).inv :=
  by
  apply Quiver.Hom.op_inj
  dsimp [truncLE'Map, truncLE'XIsoCycles]
  rw [assoc, assoc, truncGE'Map_f_eq_opcyclesMap _ e.op (by simpa) h, opcyclesOpIso_inv_naturality_assoc,
    Iso.hom_inv_id_assoc]

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