Theorems · Theorem · category theory
CategoryTheory.op_id
∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] {X : C},
(CategoryTheory.CategoryStruct.id X).op = CategoryTheory.CategoryStruct.id (Opposite.op X)- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- Oppositestatement · cited by 8,081
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.CategoryStructstatement and proof · cited by 343
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.op_invproof · cited by 7
- CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_appproof · cited by 2
- CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_appproof · cited by 2
- AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen'proof · cited by 2
- CategoryTheory.oppositeShiftFunctorAdd_hom_appproof · cited by 1
- CategoryTheory.Functor.IsDenseSubsite.mapPreimage_idproof · cited by 1
- CategoryTheory.presheafHom_isSheafForproof · cited by 1
- CategoryTheory.oppositeShiftFunctorZero_hom_appproof · cited by 0
- AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHomproof · cited by 0