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Theorems · Definition · category theory

CategoryTheory.Functor.PreOneHypercoverDenseData.f

{C₀ : Type u₀} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v₀, u₀} C₀] →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        {F : CategoryTheory.Functor C₀ C} →
          {S : C} → (self : F.PreOneHypercoverDenseData S) → (i : self.I₀) → F.obj (self.X i) ⟶ S

the morphisms in the covering of S

Defined in
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense
Cited by
33 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.Functor.PreOneHypercoverDenseData.toPreOneHypercover · cited by 17PreOneHypercoverDenseData…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap · cited by 13essSurj.presheafMapCategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π · cited by 5essSurj.presheafMap_πCategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv · cited by 5presheafObjObjIso.invCategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.fac · cited by 3SieveStruct.facCategoryTheory.Functor.OneHypercoverDenseData.mem₁₀ · cited by 3OneHypercoverDenseData.me…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_mapPreimage_condition · cited by 3essSurj.presheafObj_mapPr…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_map · cited by 3essSurj.restriction_mapCategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_π · cited by 3presheafObjObjIso.inv_πCategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_hom · cited by 2essSurj.presheafMap_presh…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_restriction · cited by 2essSurj.presheafMap_restr…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_eq_of_fac · cited by 2essSurj.restriction_eq_of…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.hom_map · cited by 2presheafObjObjIso.hom_mapCategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_restriction · cited by 2presheafObjObjIso.inv_res…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_comp · cited by 1essSurj.presheafMap_compCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.PreOneHypercoverDenseData.I₀ · cited by 45PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData.X · cited by 44PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData · cited by 27Functor.PreOneHypercoverD…PreOneHypercoverDenseData.fCITED BYCITES

Cites7

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Cited by46

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