Theorems · Definition · category theory
SheafOfModules.Hom.val
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{J : CategoryTheory.GrothendieckTopology C} →
{R : CategoryTheory.Sheaf J RingCat} → {X Y : SheafOfModules R} → X.Hom Y → (X.val ⟶ Y.val)a morphism between the underlying presheaves of modules
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 39 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.
Cites13
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.Functorstatement · cited by 16,252
- Oppositestatement · cited by 8,081
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.Presheaf.IsSheafstatement · cited by 991
- CategoryTheory.Sheafstatement and proof · cited by 763
- RingCatstatement and proof · cited by 473
- PresheafOfModulesstatement · cited by 247
- SheafOfModulesstatement and proof · cited by 188
- SheafOfModules.valstatement · cited by 55
Cited by45
Results whose statement or proof uses this declaration.
- SheafOfModules.pushforwardproof · cited by 45
- AlgebraicGeometry.Scheme.Modules.Hom.appproof · cited by 26
- SheafOfModules.sectionsMapproof · cited by 12
- SheafOfModules.forgetproof · cited by 10
- SheafOfModules.hom_extstatement and proof · cited by 7
- SheafOfModules.forgetToSheafModuleCatproof · cited by 2
- SheafOfModules.restrictScalarsproof · cited by 2
- SheafOfModules.Hom.extstatement and proof · cited by 2
- SheafOfModules.comp_valstatement · cited by 1
- SheafOfModules.freeHomEquiv_symm_compproof · cited by 1
- SheafOfModules.pushforward_comp_idproof · cited by 1
- SheafOfModules.pushforward_id_compproof · cited by 1