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Theorems · Definition · category theory

CategoryTheory.Functor.PreOneHypercoverDenseData.X

{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) → self.I₀ → C₀

the objects in the covering of S

Defined in
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense
Cited by
44 results in Mathlib
Foundations
Depth 4 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.f · cited by 33PreOneHypercoverDenseData…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjπ · cited by 23essSurj.presheafObjπCategoryTheory.Functor.PreOneHypercoverDenseData.toPreOneHypercover · cited by 17PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex · cited by 11PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData.p₁ · cited by 10PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData.p₂ · cited by 10PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData.sieve₁₀ · cited by 8PreOneHypercoverDenseData…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_π · cited by 5essSurj.presheafMap_πCategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_hom_ext · cited by 5essSurj.presheafObj_hom_e…CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.q · cited by 4SieveStruct.qCategoryTheory.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.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.PreOneHypercoverDenseData.I₀ · cited by 45PreOneHypercoverDenseData…CategoryTheory.Functor.PreOneHypercoverDenseData · cited by 27Functor.PreOneHypercoverD…PreOneHypercoverDenseData.XCITED BYCITES

Cites4

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Cited by63

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