Mathlib Map

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 X

a family of linear maps M₁.obj X ⟶ M₂.obj X for all X.

Defined in
Mathlib.Algebra.Category.ModuleCat.Presheaf
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.

AlgebraicGeometry.Scheme.Modules.Hom.app · cited by 26Hom.appPresheafOfModules.toPresheaf · cited by 24PresheafOfModules.toPresh…PresheafOfModules.evaluation · cited by 17PresheafOfModules.evaluat…PresheafOfModules.hom_ext · cited by 14PresheafOfModules.hom_extPresheafOfModules.restrictScalars · cited by 14PresheafOfModules.restric…PresheafOfModules.Derivation.postcomp · cited by 7Derivation.postcompPresheafOfModules.comp_app · cited by 5PresheafOfModules.comp_appPresheafOfModules.sectionsMap · cited by 3PresheafOfModules.section…PresheafOfModules.ModuleColimit.map_apply · cited by 3ModuleColimit.map_applyPresheafOfModules.pushforward₀ · cited by 2PresheafOfModules.pushfor…PresheafOfModules.Hom.ext · cited by 2Hom.extPresheafOfModules.Hom.naturality · cited by 2Hom.naturalityPresheafOfModules.freeYonedaCoproductMk · cited by 1PresheafOfModules.freeYon…PresheafOfModules.freeYonedaEquiv_symm_app · cited by 1PresheafOfModules.freeYon…PresheafOfModules.id_app · cited by 1PresheafOfModules.id_appCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeModuleCat · cited by 1429ModuleCatRingCat · cited by 473RingCatRingCat.carrier · cited by 279RingCat.carrierPresheafOfModules · cited by 247PresheafOfModulesPresheafOfModules.obj · cited by 186PresheafOfModules.objPresheafOfModules.Hom · cited by 8PresheafOfModules.HomHom.appCITED BYCITES

Cites11

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Cited by99

Results whose statement or proof uses this declaration.