Mathlib Map

Theorems · Inductive type · category theory

CategoryTheory.MonoidalClosed

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

A monoidal category C is (right) monoidal closed if every object is (right) closed.

Defined in
Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by
134 results in Mathlib
Foundations
Depth 2 from the axioms, rests on 3 definitions · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.MonoidalClosed.internalHom · cited by 23MonoidalClosed.internalHomCategoryTheory.MonoidalCategory.DayConvolutionInternalHom · cited by 17MonoidalCategory.DayConvo…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.π · cited by 14DayConvolutionInternalHom…CategoryTheory.MonoidalCategory.Arrow.pullbackHom · cited by 12Arrow.pullbackHomCategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf · cited by 10MonoidalClosed.enrichedOr…CategoryTheory.MonoidalCategory.dayConvolutionInternalHomDiagramFunctor · cited by 10MonoidalCategory.dayConvo…CategoryTheory.Functor.closedIhom · cited by 9Functor.closedIhomCategoryTheory.ExponentialIdeal · cited by 8CategoryTheory.Exponentia…CategoryTheory.InternallyProjective · cited by 8CategoryTheory.Internally…CategoryTheory.MonoidalClosed.internalHomAdjunction₂ · cited by 7MonoidalClosed.internalHo…CategoryTheory.expComparison · cited by 7CategoryTheory.expCompari…CategoryTheory.Pi.ihom · cited by 7Pi.ihomCategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app · cited by 5DayConvolutionInternalHom…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_app · cited by 5DayConvolutionInternalHom…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.hπ · cited by 5DayConvolutionInternalHom…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalClosedCITED BYCITES

Cites2

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

Cited by207

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 207.