Theorems · Definition · category theory

CategoryTheory.IsGrothendieckAbelian.tensorObjPreadditiveCoyonedaObjAdjunction

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.IsGrothendieckAbelian.{v, v, u} C] →
        (G : C) → CategoryTheory.IsGrothendieckAbelian.tensorObj G ⊣ CategoryTheory.preadditiveCoyonedaObj G

The tensor-hom adjunction (· ⊗ G) ⊣ Hom(G, ·).

Defined in: Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu
Cited by: 1 results in Mathlib
Foundations: Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.IsGrothendieckAbelian

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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.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Abelianstatement and proof · cited by 1,753
ModuleCatstatement · cited by 1,429
MulOppositestatement · cited by 1,135
CategoryTheory.Adjunctionstatement · cited by 524
CategoryTheory.Endstatement · cited by 169
CategoryTheory.IsGrothendieckAbelianstatement and proof · cited by 30
CategoryTheory.Adjunction.ofIsRightAdjointproof · cited by 13
CategoryTheory.preadditiveCoyonedaObjstatement and proof · cited by 11
CategoryTheory.IsGrothendieckAbelian.tensorObjstatement · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimitsproof · cited by 0