Theorems · Definition · category theory
CategoryTheory.Limits.Types.pullbackIsoPullback
{X Y Z : Type u} →
(f : X ⟶ Z) → (g : Y ⟶ Z) → CategoryTheory.Limits.pullback f g ≅ CategoryTheory.Limits.Types.PullbackObj f gThe pullback given by the instance HasPullbacks (Type u) is isomorphic to the
explicit pullback object given by PullbackObj.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.pullbackstatement · cited by 864
- CategoryTheory.Limits.WalkingCospanstatement · cited by 496
- CategoryTheory.Limits.cospanstatement · cited by 467
- Equiv.toIsoproof · cited by 58
- CategoryTheory.Limits.Types.PullbackObjstatement · cited by 17
- CategoryTheory.Limits.pullbackIsPullbackproof · cited by 14
- CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObjproof · cited by 7
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fststatement · cited by 3
- CategoryTheory.Limits.Types.pullbackIsoPullback_inv_sndstatement · cited by 3
- CategoryTheory.PreGaloisCategory.fiberPullbackEquivproof · cited by 3
- CategoryTheory.Limits.Types.range_fst_of_isPullbackproof · cited by 2
- CategoryTheory.Limits.Types.pullbackIsoPullback_hom_fststatement · cited by 1
- CategoryTheory.Limits.Types.pullbackIsoPullback_hom_sndstatement · cited by 1
- CategoryTheory.Limits.Concrete.pullbackEquivproof · cited by 1
- CategoryTheory.Limits.Concrete.pullbackMk_fstproof · cited by 1
- CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_fst_applyproof · cited by 1
- CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_snd_applyproof · cited by 1
- CategoryTheory.Limits.Concrete.pullbackMk_sndproof · cited by 1
- AlgebraicGeometry.Scheme.pullbackComparison_forget_surjectiveproof · cited by 0