homEquiv — Mathlib

English

For CatEnriched C and 1-cells f ≫ f', g ≫ g', h ≫ h', the horizontal composition associator is compatible in HEq: HEq (hComp (hComp η θ) κ) (hComp η (hComp θ κ)).

Русский

Для CatEnriched C и 1-морфизмов f ≫ f', g ≫ g', h ≫ h' горизонтальная композиционная ассоциативность совместима в HEq: HEq (hComp (hComp η θ) κ) (hComp η (hComp θ κ)).

LaTeX

$$$ HEq\\left( \\mathrm{hComp}(\\mathrm{hComp} \\eta \\theta, \\kappa) , \\mathrm{hComp}(\\eta, \\mathrm{hComp}(\\theta, \\kappa))\\right) $$$

Lean4

/-- The hom-types in a `Cat`-enriched ordinary category are equivalent to the types underlying the
hom-categories. -/
def homEquiv {a b : CatEnrichedOrdinary C} : (a ⟶ b) ≃ (a.toBase ⟶ b.toBase) :=
  (eHomEquiv (V := Cat)).trans Cat.fromChosenTerminalEquiv

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