π_map — Mathlib

English

The projection π and the homology map commute with the cycles map via the canonical compatibility: π_A(n) ≫ map(f, φ, n) = cyclesMap(f, φ, n) ≫ π_B(n).

Русский

Проекция π и отображение гомологии commute через cyclesMap: π_A(n) ≫ map(f, φ, n) = cyclesMap(f, φ, n) ≫ π_B(n).

LaTeX

$$$\pi_A(n) \circ \mathrm{map}(f, \phi, n) = \mathrm{cyclesMap}(f, \phi, n) \circ \pi_B(n)$$$

Lean4

@[reassoc, elementwise]
theorem π_map (n : ℕ) : π A n ≫ map f φ n = cyclesMap f φ n ≫ π B n := by simp [map, cyclesMap]

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