isomorphisms_op — Mathlib

English

The isomorphisms property commutes with taking opposites: isomorphisms(C).op = isomorphisms(C^op).

Русский

Свойство изоморфизмов сохраняется при противоположности: isomorphisms(C).op = isomorphisms(C^op).

LaTeX

$$$\\mathrm{isomorphisms}(C)^{\\mathrm{op}} = \\mathrm{isomorphisms}(C^{\\mathrm{op}})$$$

Lean4

theorem isomorphisms_op : (isomorphisms C).op = isomorphisms Cᵒᵖ :=
  by
  ext X Y f
  simp only [op, isomorphisms.iff]
  exact ⟨fun _ ↦ inferInstanceAs (IsIso f.unop.op), fun _ ↦ inferInstance⟩

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