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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 → Prop

A 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
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.HasGlobalSectionsFunctor · cited by 14CategoryTheory.HasGlobalS…CategoryTheory.Adjunction.isLeftAdjoint · cited by 10Adjunction.isLeftAdjointCategoryTheory.Adjunction.ofIsLeftAdjoint · cited by 9Adjunction.ofIsLeftAdjointCategoryTheory.Functor.rightAdjoint · cited by 5Functor.rightAdjointCategoryTheory.Functor.isLeftAdjoint_of_iso · cited by 2Functor.isLeftAdjoint_of_…CategoryTheory.isLeftAdjoint_of_costructuredArrowTerminals · cited by 2CategoryTheory.isLeftAdjo…CategoryTheory.Limits.hasLimitsOfShape_iff_isLeftAdjoint_const · cited by 2Limits.hasLimitsOfShape_i…CategoryTheory.Adjunction.isCardinalFilteredGenerator · cited by 1Adjunction.isCardinalFilt…CategoryTheory.Functor.isLeftAdjoint_of_rightAdjointObjIsDefined_eq_top · cited by 1Functor.isLeftAdjoint_of_…CategoryTheory.Adjunction.preservesColimitsOfShape_iff · cited by 1Adjunction.preservesColim…CategoryTheory.isLeftAdjoint_iff_hasTerminal_costructuredArrow · cited by 1CategoryTheory.isLeftAdjo…CategoryTheory.isLeftAdjoint_of_preservesColimits_of_isSeparating · cited by 1CategoryTheory.isLeftAdjo…CategoryTheory.isLeftAdjoint_triangle_lift · cited by 1CategoryTheory.isLeftAdjo…CategoryTheory.isLeftAdjoint_triangle_lift_comonadic · cited by 1CategoryTheory.isLeftAdjo…SheafOfModules.isQuasicoherent_pushforward_of_isLeftAdjoint · cited by 1SheafOfModules.isQuasicoh…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorFunctor.IsLeftAdjointCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by35

Results whose statement or proof uses this declaration.