Theorems · Theorem · category theory
SheafOfModules.sectionsFunctor_map
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
(R : CategoryTheory.Sheaf J RingCat) {X Y : SheafOfModules R} (f : X ⟶ Y),
(SheafOfModules.sectionsFunctor R).map f = TypeCat.ofHom (SheafOfModules.sectionsMap f)- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
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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 and proof · cited by 32,603
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Sheafstatement and proof · cited by 763
- RingCatstatement and proof · cited by 473
- TypeCat.ofHomstatement · cited by 389
- SheafOfModulesstatement and proof · cited by 188
- SheafOfModules.sectionsstatement · cited by 28
- SheafOfModules.sectionsMapstatement · cited by 12
- SheafOfModules.sectionsFunctorstatement and proof · cited by 2
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