lcurry — Mathlib

English

The heterobasic lcurry is compatible with composition in a natural way, respecting the bilinear structure.

Русский

Гетеробазовая lcurry совместима с композициями, уважая билинейную структуру.

LaTeX

$$$\text{lcurry}(f \circ g) = \text{lcurry}(f) \circ \text{lcurry}(g)$$$

Lean4

/-- Heterobasic version of `TensorProduct.lcurry`:

Given a linear map `M ⊗[R] N →[A] P`, compose it with the canonical
bilinear map `M →[A] N →[R] M ⊗[R] N` to form a bilinear map `M →[A] N →[R] P`. -/
@[simps]
def lcurry : (M ⊗[R] N →ₗ[A] P) →ₗ[B] M →ₗ[A] N →ₗ[R] P
    where
  toFun := curry
  map_add' _ _ := rfl
  map_smul' _ _ := rfl

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