Theorems · Definition · category theory
Quiver.Hom.mop
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (X ⟶ Y) → ({ unmop := X } ⟶ { unmop := Y })The monoidal opposite of a morphism f : X ⟶ Y is just f, thought of as mop X ⟶ mop Y.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Opposite
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.MonoidalOppositestatement · cited by 179
Cited by35
Results whose statement or proof uses this declaration.
- CategoryTheory.mopFunctorproof · cited by 24
- MonObj.mopEquivproof · cited by 14
- CategoryTheory.leftDualFunctorproof · cited by 2
- CategoryTheory.rightDualFunctorproof · cited by 2
- Quiver.Hom.unmop_injproof · cited by 1
- Quiver.Hom.mop_injstatement and proof · cited by 0
- Quiver.Hom.mop_unmopstatement · cited by 0
- CategoryTheory.MonoidalOpposite.mop_hom_braidingstatement · cited by 0