Theorems · Definition · category theory
CategoryTheory.leftAdjointMate
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] →
{X Y : C} →
[inst_2 : CategoryTheory.HasLeftDual X] → [inst_3 : CategoryTheory.HasLeftDual Y] → (X ⟶ Y) → (ᘁY ⟶ ᘁX)The left adjoint mate ᘁf : ᘁY ⟶ ᘁX of a morphism f : X ⟶ Y.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftproof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
- CategoryTheory.MonoidalCategoryStruct.associatorproof · cited by 667
- CategoryTheory.MonoidalCategoryStruct.leftUnitorproof · cited by 437
- CategoryTheory.MonoidalCategoryStruct.rightUnitorproof · cited by 397
- CategoryTheory.ExactPairing.coevaluationproof · cited by 29
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.leftDualFunctorproof · cited by 2
- CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluationstatement · cited by 1
- CategoryTheory.leftAdjointMate_compstatement · cited by 1
- CategoryTheory.leftAdjointMate_comp_evaluationstatement and proof · cited by 1
- CategoryTheory.leftAdjointMate_idstatement · cited by 1
- CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeftstatement · cited by 1
- CategoryTheory.coevaluation_comp_leftAdjointMatestatement and proof · cited by 1
- CategoryTheory.comp_leftAdjointMatestatement and proof · cited by 1
- CategoryTheory.leftDualIsoproof · cited by 1
- CategoryTheory.leftAdjointMate_comp_evaluation_assocstatement and proof · cited by 0
- CategoryTheory.coevaluation_comp_leftAdjointMate_assocstatement and proof · cited by 0
- CategoryTheory.comp_leftAdjointMate_assocstatement and proof · cited by 0