Theorems · Theorem · category theory
CategoryTheory.isIso_unop_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : Cᵒᵖ} (f : X ⟶ Y),
CategoryTheory.IsIso f.unop ↔ CategoryTheory.IsIso f- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- Oppositestatement and proof · cited by 8,081
- Opposite.unopstatement and proof · cited by 2,231
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- Quiver.Hom.unopstatement and proof · cited by 903
- CategoryTheory.isIso_op_iffproof · cited by 5
- Quiver.Hom.op_unopproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isDetecting_op_iffproof · cited by 2
- CategoryTheory.ObjectProperty.isCodetecting_op_iffproof · cited by 2
- CategoryTheory.MorphismProperty.op_isomorphismsproof · cited by 2
- CategoryTheory.isArtinianObject_iff_isEventuallyConstantproof · cited by 1
- CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_objproof · cited by 0