Theorems · Definition · category theory
PresheafOfModules.Hom.app
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{R : CategoryTheory.Functor Cᵒᵖ RingCat} →
{M₁ M₂ : PresheafOfModules R} → M₁.Hom M₂ → (X : Cᵒᵖ) → M₁.obj X ⟶ M₂.obj Xa family of linear maps M₁.obj X ⟶ M₂.obj X for all X.
- Cited by
- 88 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- ModuleCatstatement · cited by 1,429
- RingCatstatement and proof · cited by 473
- RingCat.carrierstatement · cited by 279
- PresheafOfModulesstatement and proof · cited by 247
- PresheafOfModules.objstatement · cited by 186
- PresheafOfModules.Homstatement and proof · cited by 8
Cited by99
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Modules.Hom.appproof · cited by 26
- PresheafOfModules.toPresheafproof · cited by 24
- PresheafOfModules.evaluationproof · cited by 17
- PresheafOfModules.hom_extstatement and proof · cited by 14
- PresheafOfModules.restrictScalarsproof · cited by 14
- PresheafOfModules.Derivation.postcompproof · cited by 7
- PresheafOfModules.comp_appstatement and proof · cited by 5
- PresheafOfModules.sectionsMapproof · cited by 3
- PresheafOfModules.ModuleColimit.map_applystatement · cited by 3
- PresheafOfModules.pushforward₀proof · cited by 2
- PresheafOfModules.Hom.extstatement and proof · cited by 2
- PresheafOfModules.Hom.naturalitystatement · cited by 2