homEquiv — Mathlib

English

Conjugation and mateEquiv commute in the specified setting.

Русский

Сопряжение и mateEquiv commute в указанной конфигурации.

LaTeX

$$$\\text{conjugateEquiv } adj_1 adj_2(α) \\circ \\text{mateEquiv } adj_1 adj_3(β) = \\text{mateEquiv } adj_2 adj_3(β) \\circ \\text{conjugateEquiv } adj_1 adj_2(α)$$$

Lean4

/-- The bijection `((F.obj X₁).obj X₂ ⟶ X₃) ≃ (X₂ ⟶ (G.obj (op X₁)).obj X₃)`
given by an adjunction with a parameter `adj₂ : F ⊣₂ G`. -/
def homEquiv : ((F.obj X₁).obj X₂ ⟶ X₃) ≃ (X₂ ⟶ (G.obj (op X₁)).obj X₃) :=
  (adj₂.adj X₁).homEquiv _ _

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