Theorems · Theorem · category theory

CategoryTheory.preadditiveCoyoneda_obj

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] (X : Cᵒᵖ),
  CategoryTheory.preadditiveCoyoneda.obj X =
    (CategoryTheory.preadditiveCoyonedaObj (Opposite.unop X)).comp
      (CategoryTheory.forget₂ (ModuleCat (CategoryTheory.End (Opposite.unop X))ᵐᵒᵖ) AddCommGrpCat)

Defined in: Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites19

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.Functor.objstatement and proof · cited by 19,642
RingHom.idstatement · cited by 18,349
CategoryTheory.Functorstatement · cited by 16,252
LinearMapstatement · cited by 10,215
Oppositestatement and proof · cited by 8,081
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Preadditivestatement and proof · cited by 3,309
AddMonoidHomstatement · cited by 3,230
Opposite.unopstatement · cited by 2,231
ModuleCatstatement · cited by 1,429
MulOppositestatement · cited by 1,135

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObjproof · cited by 1