lift_apply — Mathlib

English

The same lift expression as above, written without the prime: lift k G A F f = f.sum (b • F(ofAdd a)).

Русский

То же выражение lift без апострофа: lift k G A F f = \\sum a b \\; b • F(ofAdd a).

LaTeX

$$$ lift\\ k\\ G\\ A\\ F\\; f = f.sum\\; (a,b) \\mapsto b \\cdot F(\\text{ofAdd}(a)) $$$

Lean4

theorem lift_apply (F : Multiplicative G →* A) (f : MonoidAlgebra k G) :
    lift k G A F f = f.sum fun a b => b • F (Multiplicative.ofAdd a) := by simp only [lift_apply', Algebra.smul_def]

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