Mathlib Map

Theorems · Definition · category theory

PresheafOfModules.free

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (R : CategoryTheory.Functor Cᵒᵖ RingCat) →
      CategoryTheory.Functor (CategoryTheory.Functor Cᵒᵖ (Type u)) (PresheafOfModules R)

The free presheaf of modules functor (Cᵒᵖ ⥤ Type u) ⥤ PresheafOfModules.{u} R.

Defined in
Mathlib.Algebra.Category.ModuleCat.Presheaf.Free
Cited by
8 results in Mathlib
Foundations
Depth 87 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.

PresheafOfModules.Elements.freeYoneda · cited by 5Elements.freeYonedaPresheafOfModules.freeYonedaEquiv · cited by 3PresheafOfModules.freeYon…PresheafOfModules.freeYoneda · cited by 2PresheafOfModules.freeYon…PresheafOfModules.freeAdjunction · cited by 2PresheafOfModules.freeAdj…PresheafOfModules.pushforwardCompCoyonedaFreeYonedaCorepresentableBy · cited by 1PresheafOfModules.pushfor…PresheafOfModules.freeYonedaEquiv_symm_app · cited by 1PresheafOfModules.freeYon…PresheafOfModules.freeYoneda.isSeparating · cited by 1freeYoneda.isSeparatingPresheafOfModules.pullbackObjIsDefined_free_yoneda · cited by 1PresheafOfModules.pullbac…PresheafOfModules.freeYonedaEquiv_comp · cited by 0PresheafOfModules.freeYon…PresheafOfModules.free_map_app · cited by 0PresheafOfModules.free_ma…PresheafOfModules.free_obj · cited by 0PresheafOfModules.free_objPresheafOfModules.freeAdjunction_homEquiv · cited by 0PresheafOfModules.freeAdj…PresheafOfModules.freeAdjunction_unit_app · cited by 0PresheafOfModules.freeAdj…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appRingCat · cited by 473RingCatRingCat.carrier · cited by 279RingCat.carrierPresheafOfModules · cited by 247PresheafOfModulesModuleCat.free · cited by 19ModuleCat.freePresheafOfModules.freeObj · cited by 7PresheafOfModules.freeObjPresheafOfModules.freeCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by13

Results whose statement or proof uses this declaration.