map_sub — Mathlib

English

For a morphism f: F ⟶ G and z: G ⟶ K of degree n, δ(n,m)((Cochain.ofHom f).comp z (zero_add n)) equals ((Cochain.ofHom f).comp (δ(n,m) z) (zero_add m)).

Русский

Для морфизма f: F ⟶ G и z: G ⟶ K, степени n, δ(n,m)((Cochain.ofHom f).comp z (zero_add n)) = ((Cochain.ofHom f).comp (δ(n,m) z) (zero_add m)).

LaTeX

$$$\\delta(n,m)((\\mathrm{Cochain.ofHom}(f)\\,\\circ\\, z)\\,(\\mathrm{zero\\_add}\\ n)) = (\\mathrm{Cochain.ofHom}(f)\\,\\circ\\, (\\delta(n,m) z))\\,(\\mathrm{zero\\_add}\\ m).$$$

Lean4

@[simp]
protected theorem map_sub : (z - z').map Φ = z.map Φ - z'.map Φ := by cat_disch

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