Theorems · Definition · category theory

CategoryTheory.IsGrothendieckAbelian.tensorObj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [CategoryTheory.IsGrothendieckAbelian.{v, v, u} C] →
        (G : C) → CategoryTheory.Functor (ModuleCat (CategoryTheory.End G)ᵐᵒᵖ) C

The left adjoint of the functor Hom(G, ·), which can be thought of as · ⊗ G.

Defined in: Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu
Cited by: 1 results in Mathlib
Foundations: Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.IsGrothendieckAbelian

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Around this declaration

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

Cites9

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.Functorstatement · cited by 16,252
CategoryTheory.Abelianstatement and proof · cited by 1,753
ModuleCatstatement · cited by 1,429
MulOppositestatement · cited by 1,135
CategoryTheory.Endstatement · cited by 169
CategoryTheory.IsGrothendieckAbelianstatement and proof · cited by 30
CategoryTheory.preadditiveCoyonedaObjproof · cited by 11
CategoryTheory.Functor.leftAdjointproof · cited by 6

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.IsGrothendieckAbelian.tensorObjPreadditiveCoyonedaObjAdjunctionstatement · cited by 1
CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimitsstatement and proof · cited by 0