Theorems · Theorem · category theory
SheafOfModules.hom_ext_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
{R : CategoryTheory.Sheaf J RingCat} {X Y : SheafOfModules R} {f g : X ⟶ Y}, f = g ↔ f.val = g.val- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites14
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.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
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