Theorems · Definition · category theory
CategoryTheory.NatTrans.unop
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
{F G : CategoryTheory.Functor Cᵒᵖ Dᵒᵖ} → (F ⟶ G) → (G.unop ⟶ F.unop)The "unopposite" of a natural transformation.
- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 21 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.unopproof · cited by 903
- CategoryTheory.Functor.unopstatement · cited by 138
Cited by28
Results whose statement or proof uses this declaration.
- CategoryTheory.NatIso.unopproof · cited by 12
- CategoryTheory.Limits.coneUnopOfCoconeproof · cited by 9
- CategoryTheory.Limits.coconeUnopOfConeproof · cited by 9
- CategoryTheory.NatIso.unop_homstatement · cited by 5
- CategoryTheory.Adjunction.leftOpproof · cited by 3
- CategoryTheory.Adjunction.rightOpproof · cited by 3
- CategoryTheory.NatTrans.Equifibered.unopstatement · cited by 2
- CategoryTheory.NatTrans.Coequifibered.unopstatement · cited by 2
- CategoryTheory.Adjunction.unopproof · cited by 2
- CategoryTheory.ObjectProperty.colimitsOfShape_eq_unop_limitsOfShapeproof · cited by 2
- CategoryTheory.ObjectProperty.limitsOfShape_eq_unop_colimitsOfShapeproof · cited by 2
- CategoryTheory.NatTrans.unop_compstatement · cited by 1