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Theorems · Definition · category theory

CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [CategoryTheory.MonoidalClosed C] → CategoryTheory.EnrichedOrdinaryCategory C C

A monoidal closed category is an enriched ordinary category over itself.

Defined in
Mathlib.CategoryTheory.Monoidal.Closed.Enrichment
Cited by
10 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosed

Around this declaration

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

CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv · cited by 2FunctorCategory.homEquivCategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv · cited by 2Presheaf.functorEnrichedH…CategoryTheory.Presheaf.isSheaf_functorEnrichedHom · cited by 1Presheaf.isSheaf_functorE…CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality · cited by 1Presheaf.functorEnrichedH…CategoryTheory.GrothendieckTopology.W.whiskerLeft · cited by 1W.whiskerLeftCategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_eHomWhiskerLeft · cited by 1MonoidalClosed.enrichedOr…CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_eHomWhiskerRight · cited by 1MonoidalClosed.enrichedOr…CategoryTheory.MonoidalClosed.FunctorCategory.closed · cited by 0FunctorCategory.closedCategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three · cited by 0FunctorCategory.homEquiv_…CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm · cited by 0FunctorCategory.homEquiv_…CategoryTheory.MonoidalClosed.FunctorCategory.monoidalClosed · cited by 0FunctorCategory.monoidalC…CategoryTheory.GrothendieckTopology.W.whiskerRight · cited by 0W.whiskerRightCategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv · cited by 0MonoidalClosed.enrichedOr…CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm · cited by 0MonoidalClosed.enrichedOr…CategoryTheory.MonoidalClosed.FunctorCategory.adj · cited by 0FunctorCategory.adjCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalClosed · cited by 134CategoryTheory.MonoidalCl…CategoryTheory.EnrichedOrdinaryCategory · cited by 109CategoryTheory.EnrichedOr…CategoryTheory.MonoidalClosed.curryHomEquiv' · cited by 4MonoidalClosed.curryHomEq…MonoidalClosed.enrichedOrdina…CITED BYCITES

Cites5

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Cited by15

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