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Theorems · Inductive type · category theory

CategoryTheory.Adjunction.Quadruple

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        CategoryTheory.Functor C D →
          CategoryTheory.Functor D C →
            CategoryTheory.Functor C D → CategoryTheory.Functor D C → Type (max (max (max u₁ u₂) v₁) v₂)

Structure containing the three adjunctions of an adjoint quadruple L ⊣ F ⊣ G ⊣ R.

Defined in
Mathlib.CategoryTheory.Adjunction.Quadruple
Cited by
16 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.Adjunction.Quadruple.leftTriple · cited by 8Quadruple.leftTripleCategoryTheory.Adjunction.Quadruple.rightTriple · cited by 8Quadruple.rightTripleCategoryTheory.Adjunction.Quadruple.op · cited by 6Quadruple.opCategoryTheory.Adjunction.Quadruple.adj₁ · cited by 4Quadruple.adj₁CategoryTheory.Adjunction.Quadruple.adj₂ · cited by 4Quadruple.adj₂CategoryTheory.Adjunction.Quadruple.adj₃ · cited by 4Quadruple.adj₃CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app · cited by 2Quadruple.epi_leftTriple_…CategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_app_iff_mono_rightTriple_rightToLeft_app · cited by 1Quadruple.epi_leftTriple_…CategoryTheory.Adjunction.Quadruple.mk.inj · cited by 1mk.injCategoryTheory.Adjunction.Quadruple.mk.noConfusion · cited by 1mk.noConfusionCategoryTheory.Adjunction.Quadruple.casesOn · cited by 0Quadruple.casesOnCategoryTheory.Adjunction.Quadruple.ctorIdx · cited by 0Quadruple.ctorIdxCategoryTheory.Adjunction.Quadruple.epi_leftTriple_leftToRight_iff_mono_rightTriple_rightToLeft · cited by 0Quadruple.epi_leftTriple_…CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_iff_mono_rightTriple_leftToRight · cited by 0Quadruple.epi_leftTriple_…CategoryTheory.Adjunction.Quadruple.leftTriple_adj₁ · cited by 0Quadruple.leftTriple_adj₁CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorAdjunction.QuadrupleCITED BYCITES

Cites2

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Cited by28

Results whose statement or proof uses this declaration.