Theorems · Definition · category theory
CategoryTheory.MonoidalClosed.curry
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] →
{A X Y : C} →
[inst_2 : CategoryTheory.Closed A] → (CategoryTheory.MonoidalCategoryStruct.tensorObj A Y ⟶ X) → (Y ⟶ A ⟹ X)Currying in a monoidal closed category.
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Adjunction.homEquivproof · cited by 202
- CategoryTheory.ihomstatement · cited by 179
- CategoryTheory.Closedstatement and proof · cited by 90
- CategoryTheory.ihom.adjunctionproof · cited by 31
Cited by56
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalClosed.uncurry_currystatement · cited by 15
- CategoryTheory.MonoidalClosed.curry'proof · cited by 14
- CategoryTheory.MonoidalClosed.compproof · cited by 13
- CategoryTheory.curryRightUnitorHomproof · cited by 8
- CategoryTheory.MonoidalClosed.idproof · cited by 7
- CategoryTheory.MonoidalClosed.ihomCurryproof · cited by 7
- CategoryTheory.MonoidalClosed.curry_natural_leftstatement · cited by 6
- CategoryTheory.MonoidalClosed.ihomUncurryproof · cited by 6
- CategoryTheory.MonoidalClosed.curry_uncurrystatement · cited by 5
- CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_appproof · cited by 5
- CategoryTheory.MonoidalClosed.comp_eqstatement · cited by 4
- CategoryTheory.Over.sectionsCurryproof · cited by 4