Theorems · Definition · category theory
CategoryTheory.Adjunction.ofIsRightAdjoint
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(right : CategoryTheory.Functor C D) → [inst_2 : right.IsRightAdjoint] → right.leftAdjoint ⊣ rightThe adjunction associated to a functor known to be a right adjoint.
- Defined in
- Mathlib.CategoryTheory.Adjunction.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Adjunctionstatement · cited by 524
- Nonempty.someproof · cited by 340
- CategoryTheory.Functor.IsRightAdjointstatement and proof · cited by 46
- CategoryTheory.Functor.leftAdjointstatement · cited by 6
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.sheafificationAdjunctionproof · cited by 30
- SheafOfModules.pullbackPushforwardAdjunctionproof · cited by 7
- PresheafOfModules.pullbackPushforwardAdjunctionproof · cited by 3
- CategoryTheory.Functor.isRightAdjoint_of_isoproof · cited by 2
- CategoryTheory.Functor.sheafAdjunctionContinuousproof · cited by 2
- CategoryTheory.HasSheafify.mk'proof · cited by 2
- CategoryTheory.Functor.isRightAdjoint_iff_leftAdjointObjIsDefined_eq_topproof · cited by 1
- CategoryTheory.isRightAdjoint_iff_hasInitial_structuredArrowproof · cited by 1
- CategoryTheory.isRightAdjoint_triangle_liftproof · cited by 1
- CategoryTheory.isRightAdjoint_triangle_lift_monadicproof · cited by 1
- CategoryTheory.IsFilteredOrEmpty.of_isRightAdjointproof · cited by 0