Theorems · Definition · category theory
CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ) CategoryTheory.Cat) →
{S : C} →
{M N : ↑(F.obj { as := Opposite.op S })} →
(M ⟶ N) ≃ (F.presheafHom M N).obj (Opposite.op (CategoryTheory.Over.mk (CategoryTheory.CategoryStruct.id S)))The bijection (M ⟶ N) ≃ (F.presheafHom M N).obj (op (Over.mk (𝟙 S))).
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- Prefunctor.objstatement and proof · cited by 1,241
- CategoryTheory.PrelaxFunctor.toPrelaxFunctorStructstatement and proof · cited by 1,154
- CategoryTheory.PrelaxFunctorStruct.toPrefunctorstatement and proof · cited by 1,142
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Catstatement and proof · cited by 884
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Pseudofunctor.bijective_toDescentData_map_iffproof · cited by 1
- CategoryTheory.Pseudofunctor.DescentData.faithful_pullFunctorproof · cited by 0
- CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_applystatement and proof · cited by 0
- CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_applystatement and proof · cited by 0