Theorems · Definition · category theory
CategoryTheory.NatTrans.rightOp
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
{F G : CategoryTheory.Functor Cᵒᵖ D} → (F ⟶ G) → (G.rightOp ⟶ F.rightOp)Given a natural transformation α : F ⟶ G, for F G : Cᵒᵖ ⥤ D,
taking op of each component gives a natural transformation G.rightOp ⟶ F.rightOp.
- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.Functor.rightOpstatement · cited by 214
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.coconeRightOpOfConeproof · cited by 16
- CategoryTheory.SimplicialObject.Augmented.rightOpproof · cited by 15
- CategoryTheory.Functor.leftOpRightOpEquivproof · cited by 15
- CategoryTheory.Limits.coneRightOpOfCoconeproof · cited by 9
- AlgebraicGeometry.Scheme.AffineZariskiSite.relativeGluingDataproof · cited by 5
- CategoryTheory.simplicialToCosimplicialAugmentedproof · cited by 4
- CategoryTheory.NatTrans.rightOpWhiskerRightstatement · cited by 1
- Extproof · cited by 1
- CategoryTheory.NatTrans.rightOpWhiskerRight_assocstatement and proof · cited by 0
- CategoryTheory.NatTrans.rightOp_appstatement and proof · cited by 0
- CategoryTheory.NatTrans.rightOp_compstatement · cited by 0
- CategoryTheory.NatTrans.rightOp_idstatement · cited by 0