comp_id_moduleCat — Mathlib

English

mkOfSMul φ is the R-module over the underlying abelian group with the scalar action defined by φ; i.e., it is the object in ModuleCat R whose carrier is the same as the carrier of the underlying abelian group.

Русский

mkOfSMul φ есть модуль над R над тем же носителем абелевой группы.

LaTeX

$$$\text{mkOfSMul}(\phi) = \mathrm{ModuleCat.of}(R, \mathrm{mkOfSMul}'\phi)$$$

Lean4

@[simp]
theorem comp_id_moduleCat {R} [Ring R] {G : ModuleCat.{u} R} {H : Type u} [AddCommGroup H] [Module R H]
    (f : G →ₗ[R] H) : f.comp (𝟙 G : G ⟶ G).hom = f := by simp

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