Theorems · Definition · category theory

CategoryTheory.Closed.adj

{C : Type u} →
  {inst : CategoryTheory.Category.{v, u} C} →
    {inst_1 : CategoryTheory.MonoidalCategory C} →
      {X : C} →
        [self : CategoryTheory.Closed X] →
          CategoryTheory.MonoidalCategory.tensorLeft X ⊣ CategoryTheory.Closed.rightAdj X

tensorLeft X is a left adjoint

Defined in: Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by: 7 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Closed

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Cites6

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
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.Adjunctionstatement · cited by 524
CategoryTheory.MonoidalCategory.tensorLeftstatement · cited by 170
CategoryTheory.Closedstatement and proof · cited by 90
CategoryTheory.Closed.rightAdjstatement · cited by 1

Cited by9

Results whose statement or proof uses this declaration.

CategoryTheory.ihom.adjunctionproof · cited by 31
CategoryTheory.MonoidalClosed.uncurry_curryproof · cited by 15
CategoryTheory.MonoidalClosed.uncurry_injectiveproof · cited by 11
CategoryTheory.MonoidalClosed.curry_uncurryproof · cited by 5
CategoryTheory.MonoidalClosed.curry_injectiveproof · cited by 3
CategoryTheory.tensorClosedproof · cited by 0
CategoryTheory.Pi.monoidalClosed_closed_adj_counitstatement and proof · cited by 0
CategoryTheory.Pi.monoidalClosed_closed_adj_unitstatement and proof · cited by 0
CategoryTheory.Functor.monoidalClosed_closed_adjstatement and proof · cited by 0