eqToHom_f — Mathlib

English

Given an equality h: P = Q in Karoubi, the underlying morphism of eqToHom h is described by composing with P.p and the equation on X.

Русский

Для равенства h: P = Q в Karoubi подмorphism eqToHom h выражается через композицию с P.p и через равенство на X.

LaTeX

$$$\text{Karoubi}.Hom(f, Q) = P.p \circ \text{eqToHom}(\mathrm{congrArg}\, X\ h)$$$

Lean4

@[simp]
theorem eqToHom_f {P Q : Karoubi C} (h : P = Q) : Karoubi.Hom.f (eqToHom h) = P.p ≫ eqToHom (congr_arg Karoubi.X h) :=
  by
  subst h
  simp only [eqToHom_refl, Karoubi.id_f, comp_id]

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