Theorems · Definition · category theory
CategoryTheory.NatTrans.op
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] → {F G : CategoryTheory.Functor C D} → (F ⟶ G) → (G.op ⟶ F.op)The opposite of a natural transformation.
- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 41 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.
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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.Functor.opstatement · cited by 997
Cited by53
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Cocone.opproof · cited by 38
- CategoryTheory.NatIso.opproof · cited by 25
- CategoryTheory.Limits.Cone.opproof · cited by 22
- CategoryTheory.Adjunction.opproof · cited by 14
- CategoryTheory.TwoSquare.opproof · cited by 14
- TopCat.Presheaf.stalkPushforwardproof · cited by 12
- CategoryTheory.Functor.sheafPushforwardContinuousNatTransproof · cited by 11
- CategoryTheory.TwoSquare.guitartExact_op_iffproof · cited by 6
- CategoryTheory.NatIso.op_homstatement · cited by 5
- CategoryTheory.Adjunction.rightOpproof · cited by 3
- CategoryTheory.Adjunction.leftOpproof · cited by 3
- CategoryTheory.NatTrans.Equifibered.opstatement · cited by 2