coe_mapCycles₁ — Mathlib

English

The map on cycles interacts with the isoCycles morphisms via a commutative diagram: cyclesMap f φ 1 followed by (isoCycles₁ B).hom equals (isoCycles₁ A).hom followed by mapCycles₁ f φ.

Русский

Отображение циклов и изоморфии образуют коммутативный диаграмму: cyclesMap f φ 1 затем (isoCycles₁ B).hom равно (isoCycles₁ A).hom затем mapCycles₁ f φ.

LaTeX

$$$ cyclesMap(f, \varphi, 1) \;\circ\; (isoCycles_1(B))^{\mathrm{hom}} = (isoCycles_1(A))^{\mathrm{hom}} \circ mapCycles_1(f, \varphi) $$$

Lean4

@[simp]
theorem coe_mapCycles₁ (x) : (mapCycles₁ f φ x).1 = chainsMap₁ f φ x :=
  rfl

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