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Theorems · Definition · category theory

CategoryTheory.ihom.coev

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      (A : C) →
        [inst_2 : CategoryTheory.Closed A] →
          CategoryTheory.Functor.id C ⟶ (CategoryTheory.MonoidalCategory.tensorLeft A).comp (CategoryTheory.ihom A)

The coevaluation natural transformation.

Defined in
Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by
19 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Closed

Around this declaration

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

CategoryTheory.Functor.closedUnit · cited by 3Functor.closedUnitCategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_app · cited by 3MonoidalClosed.whiskerLef…CategoryTheory.Pi.closedUnit · cited by 2Pi.closedUnitCategoryTheory.ihom.ev_coev_assoc · cited by 2ihom.ev_coev_assocCategoryTheory.MonoidalClosed.coev_app_comp_pre_app · cited by 1MonoidalClosed.coev_app_c…CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc · cited by 1MonoidalClosed.coev_app_c…CategoryTheory.MonoidalClosed.curry_eq · cited by 1MonoidalClosed.curry_eqCategoryTheory.ihom.coev_ev · cited by 1ihom.coev_evCategoryTheory.ihom.coev_naturality · cited by 1ihom.coev_naturalityCategoryTheory.ihom.coev_naturality_assoc · cited by 1ihom.coev_naturality_assocCategoryTheory.ihom.ev_coev · cited by 1ihom.ev_coevCategoryTheory.Monoidal.Reflective.isIso_tfae · cited by 0Reflective.isIso_tfaeCategoryTheory.Pi.closedUnit_app · cited by 0Pi.closedUnit_appCategoryTheory.coev_expComparison · cited by 0CategoryTheory.coev_expCo…CategoryTheory.Functor.ihom_coev_app · cited by 0Functor.ihom_coev_appCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Adjunction.unit · cited by 387Adjunction.unitCategoryTheory.ihom · cited by 179CategoryTheory.ihomCategoryTheory.MonoidalCategory.tensorLeft · cited by 170MonoidalCategory.tensorLe…CategoryTheory.Closed · cited by 90CategoryTheory.ClosedCategoryTheory.ihom.adjunction · cited by 31ihom.adjunctionihom.coevCITED BYCITES

Cites11

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

Cited by21

Results whose statement or proof uses this declaration.