Theorems · Definition · category theory
CategoryTheory.Functor.leftAdjoint
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(R : CategoryTheory.Functor D C) → [R.IsRightAdjoint] → CategoryTheory.Functor C DA chosen left adjoint to a functor that is a right adjoint.
- Defined in
- Mathlib.CategoryTheory.Adjunction.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Functor.IsRightAdjointstatement and proof · cited by 46
- CategoryTheory.Functor.IsRightAdjoint.exists_leftAdjointproof · cited by 0
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.presheafToSheafproof · cited by 57
- CategoryTheory.Adjunction.ofIsRightAdjointstatement · cited by 13
- SheafOfModules.pullbackproof · cited by 12
- PresheafOfModules.pullbackproof · cited by 3
- CategoryTheory.Functor.isRightAdjoint_of_isoproof · cited by 2
- CategoryTheory.Functor.sheafPullbackproof · cited by 2
- CategoryTheory.isRightAdjoint_triangle_liftproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.tensorObjproof · cited by 1
- CategoryTheory.solutionSetCondition_of_isRightAdjointproof · cited by 0
- CategoryTheory.isRightAdjoint_square_liftstatement · cited by 0
- CategoryTheory.HasSheafify.casesOnstatement and proof · cited by 0
- CategoryTheory.HasSheafify.isLeftExactstatement · cited by 0