Theorems · Inductive type · category theory
CategoryTheory.Precoverage.HasPullbacks
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Precoverage C → PropA precoverage has pullbacks, if every covering presieve has pullbacks along arbitrary morphisms.
- Defined in
- Mathlib.CategoryTheory.Sites.Precoverage
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Precoveragestatement · cited by 204
Cited by31
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.toCoveragestatement and proof · cited by 7
- CategoryTheory.MorphismProperty.IsLocalAtTarget.mk_of_iff_of_zeroHypercoverstatement and proof · cited by 4
- CategoryTheory.MorphismProperty.IsLocalAtTarget.iff_of_zeroHypercoverstatement and proof · cited by 3
- CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderCompositionstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.iff_of_zeroHypercover_targetstatement · cited by 3
- CategoryTheory.over_toGrothendieck_eq_toGrothendieck_comap_forgetstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.toGrothendieck_comap_forget_eq_restrictedTopologystatement and proof · cited by 2
- CategoryTheory.MorphismProperty.of_zeroHypercover_targetstatement and proof · cited by 2
- CategoryTheory.Precoverage.locallyCoverDense_of_map_functorPullback_memstatement and proof · cited by 2
- CategoryTheory.Precoverage.toGrothendieck_comap_eq_restrictedTopologystatement and proof · cited by 2
- CategoryTheory.MorphismProperty.locallyCoverDense_forget_of_lestatement and proof · cited by 2
- CategoryTheory.Precoverage.hasPairwisePullbacks_of_memstatement and proof · cited by 1