cyclesMap_comp — Mathlib

English

Cycles maps are functorial with respect to composition: cyclesMap(φ1 ≫ φ2) equals cyclesMap φ1 composed with cyclesMap φ2.

Русский

Циклические отображения функториальны по отношению к композиции: cyclesMap(φ1 ≫ φ2) = cyclesMap φ1 ∘ cyclesMap φ2.

LaTeX

$$cyclesMap(φ1 ≫ φ2) = cyclesMap(φ1) ≫ cyclesMap(φ2)$$

Lean4

@[reassoc]
theorem cyclesMap_comp [HasLeftHomology S₁] [HasLeftHomology S₂] [HasLeftHomology S₃] (φ₁ : S₁ ⟶ S₂) (φ₂ : S₂ ⟶ S₃) :
    cyclesMap (φ₁ ≫ φ₂) = cyclesMap φ₁ ≫ cyclesMap φ₂ :=
  cyclesMap'_comp _ _ _ _ _

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