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Theorems · Definition · category theory

PresheafOfModules.unitHomEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {R : CategoryTheory.Functor Cᵒᵖ RingCat} → (M : PresheafOfModules R) → (PresheafOfModules.unit R ⟶ M) ≃ M.sections

The bijection (unit R ⟶ M) ≃ M.sections for M : PresheafOfModules R.

Defined in
Mathlib.Algebra.Category.ModuleCat.Presheaf
Cited by
1 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SheafOfModules.unitHomEquiv · cited by 6SheafOfModules.unitHomEqu…PresheafOfModules.unitHomEquiv_apply_coe · cited by 0PresheafOfModules.unitHom…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorEquiv · cited by 8337EquivOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homLinearEquiv.symm · cited by 1461LinearEquiv.symmModuleCat.carrier · cited by 997ModuleCat.carrierRingCat · cited by 473RingCatRingCat.carrier · cited by 279RingCat.carrierPresheafOfModules · cited by 247PresheafOfModulesModuleCat.ofHom · cited by 200ModuleCat.ofHomPresheafOfModules.obj · cited by 186PresheafOfModules.objPresheafOfModules.unitHomEquivCITED BYCITES

Cites20

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Cited by2

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