mk_id_comp — Mathlib

English

Composing with the left identity does nothing: mk_W(id_X) composed with α equals α.

Русский

Соединение с левым тождественным на X не изменяет α: mk_W(id_X) ⋅ α = α.

LaTeX

$$$\mathrm{mk}\,W\,\mathrm{id}_X \circ \alpha = \alpha$$$

Lean4

@[simp]
theorem mk_id_comp [HasSmallLocalizedHom.{w} W X Y] [HasSmallLocalizedHom.{w} W X X] (α : SmallHom.{w} W X Y) :
    (mk W (𝟙 X)).comp α = α :=
  (equiv W W.Q).injective (by simp [equiv_comp])

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