Theorems · Theorem · category theory
CategoryTheory.Adjunction.isLeftAdjoint
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G), F.IsLeftAdjoint- Defined in
- Mathlib.CategoryTheory.Adjunction.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
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.Adjunctionstatement and proof · cited by 524
- CategoryTheory.Functor.IsLeftAdjointstatement · cited by 28
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.isCardinalFilteredGeneratorproof · cited by 1
- CategoryTheory.isLeftAdjoint_triangle_lift_comonadicproof · cited by 1
- CategoryTheory.Adjunction.preservesColimitsOfShape_iffproof · cited by 1
- CategoryTheory.Functor.isLeftAdjoint_of_rightAdjointObjIsDefined_eq_topproof · cited by 1
- CategoryTheory.Localization.hasProductsOfShapeproof · cited by 1
- CategoryTheory.isLeftAdjoint_square_liftproof · cited by 0
- CategoryTheory.isLeftAdjoint_square_lift_comonadicproof · cited by 0
- CategoryTheory.Adjunction.Triple.epi_rightToLeft_app_iffproof · cited by 0
- CategoryTheory.Adjunction.preservesColimitsOfSize_iffproof · cited by 0
- CategoryTheory.MorphismProperty.isLeftAdjoint_pushoutproof · cited by 0