Theorems · Inductive type · category theory
CategoryTheory.Functor.IsLeftAdjoint
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → PropA class asserting the existence of a right adjoint.
- Defined in
- Mathlib.CategoryTheory.Adjunction.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
Cited by35
Results whose statement or proof uses this declaration.
- CategoryTheory.HasGlobalSectionsFunctorproof · cited by 14
- CategoryTheory.Adjunction.isLeftAdjointstatement · cited by 10
- CategoryTheory.Adjunction.ofIsLeftAdjointstatement and proof · cited by 9
- CategoryTheory.Functor.rightAdjointstatement and proof · cited by 5
- CategoryTheory.Functor.isLeftAdjoint_of_isostatement and proof · cited by 2
- CategoryTheory.isLeftAdjoint_of_costructuredArrowTerminalsstatement · cited by 2
- CategoryTheory.Limits.hasLimitsOfShape_iff_isLeftAdjoint_conststatement · cited by 2
- CategoryTheory.Adjunction.isCardinalFilteredGeneratorproof · cited by 1
- CategoryTheory.Functor.isLeftAdjoint_of_rightAdjointObjIsDefined_eq_topstatement · cited by 1
- CategoryTheory.Adjunction.preservesColimitsOfShape_iffproof · cited by 1
- CategoryTheory.isLeftAdjoint_iff_hasTerminal_costructuredArrowstatement and proof · cited by 1
- CategoryTheory.isLeftAdjoint_of_preservesColimits_of_isSeparatingstatement · cited by 1