flip — Mathlib

English

For an equivalence e: N ≃ Dual M, the composition e.trans e.flip.symm.dualMap realizes the evaluation on N: e.trans(e.flip.symm.dualMap) = eval on N.

Русский

Для эквивалентности e: N ≃ Dual M композиция e.trans e.flip.symm.dualMap реализует оценку на N.

LaTeX

$$$e\\,\\text{trans}\\, e.flip.symm.dualMap = \\mathrm{Dual.eval}(R,N).$$$

Lean4

/-- For a reflexive module `M`, an equivalence `N ≃ₗ[R] Dual R M` naturally yields an equivalence
`M ≃ₗ[R] Dual R N`. Such equivalences are known as perfect pairings. -/
def flip : M ≃ₗ[R] Dual R N :=
  (evalEquiv R M).trans e.dualMap

Похожие утверждения