Theorems · Theorem · category theory
CategoryTheory.isIso_of_op
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) [CategoryTheory.IsIso f.op],
CategoryTheory.IsIso fIf f.op is an isomorphism f must be too.
(This cannot be an instance as it would immediately loop!)
- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Oppositestatement · cited by 8,081
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- Quiver.Hom.unopproof · cited by 903
- CategoryTheory.invproof · cited by 467
- CategoryTheory.IsIso.hom_inv_idproof · cited by 97
- CategoryTheory.IsIso.inv_hom_idproof · cited by 88
- Quiver.Hom.op_injproof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.isIso_op_iffproof · cited by 5
- CategoryTheory.ShortComplex.quasiIso_opMap_iffproof · cited by 4