Theorems · Theorem · category theory
CategoryTheory.Precoverage.HasPullbacks.hasPullbacks_of_mem
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {J : CategoryTheory.Precoverage C} [self : J.HasPullbacks]
{X Y : C} {R : CategoryTheory.Presieve Y} (f : X ⟶ Y), R ∈ J.coverings Y → R.HasPullbacks f- Defined in
- Mathlib.CategoryTheory.Sites.Precoverage
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Presievestatement · cited by 449
- CategoryTheory.Precoveragestatement and proof · cited by 204
- CategoryTheory.Precoverage.coveringsstatement · cited by 194
- CategoryTheory.Precoverage.HasPullbacksstatement and proof · cited by 28
- CategoryTheory.Presieve.HasPullbacksstatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.hasPullbacks_of_memproof · cited by 1