mapHomologicalComplex_id — Mathlib

English

For any natural transformation α between functors F and G, the map on homological complexes commutes with f: (F.mapHomologicalComplex c).map f ≫ (map α c).app D = (map α c).app C ≫ (G.mapHomologicalComplex c).map f.

Русский

Для любой натуральной трансформации α между F и G выполняется: map f commute with α.

LaTeX

$$$(F.mapHomologicalComplex c).map f \; \circ \big( (\mathrm{mapHomologicalComplex} \alpha c)\!\app D \big) = \big( (\mathrm{mapHomologicalComplex} \alpha c)\!\app C \big) \circ (G.mapHomologicalComplex c).map f$$$

Lean4

@[simp]
theorem mapHomologicalComplex_id (c : ComplexShape ι) (F : W₁ ⥤ W₂) [F.PreservesZeroMorphisms] :
    NatTrans.mapHomologicalComplex (𝟙 F) c = 𝟙 (F.mapHomologicalComplex c) := by cat_disch

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