Theorems · Definition · category theory
CategoryTheory.Limits.WidePullback.base
{J : Type w} →
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{B : C} →
{objs : J → C} →
(arrows : (j : J) → objs j ⟶ B) →
[inst_1 : CategoryTheory.Limits.HasWidePullback B objs arrows] →
CategoryTheory.Limits.widePullback B objs arrows ⟶ BThe unique map to the base from the pullback.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Limits.limit.πproof · cited by 278
- CategoryTheory.Limits.HasWidePullbackstatement and proof · cited by 44
- CategoryTheory.Limits.widePullbackstatement · cited by 31
- CategoryTheory.Limits.WidePullbackShape.wideCospanproof · cited by 22
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.Arrow.cechNerveproof · cited by 18
- CategoryTheory.Arrow.augmentedCechNerveproof · cited by 16
- CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.sproof · cited by 6
- CategoryTheory.Arrow.mapCechNerveproof · cited by 3
- CategoryTheory.Limits.WidePullback.lift_basestatement · cited by 2
- CategoryTheory.Limits.WidePullback.π_arrowstatement · cited by 2
- CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_basestatement and proof · cited by 1
- CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0statement and proof · cited by 1
- CategoryTheory.Limits.Concrete.widePullback_extstatement and proof · cited by 1
- CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succproof · cited by 1
- CategoryTheory.Limits.WidePullback.hom_extstatement and proof · cited by 1
- CategoryTheory.Limits.WidePullback.lift_base_assocstatement and proof · cited by 0