Theorems · Theorem · category theory
TopCat.pullbackIsoProdSubtype_inv_snd_apply
∀ {X Y Z : TopCat} (f : X ⟶ Z) (g : Y ⟶ Z)
(x : { p // (CategoryTheory.ConcreteCategory.hom f) p.1 = (CategoryTheory.ConcreteCategory.hom g) p.2 }),
(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pullback.snd f g))
((CategoryTheory.ConcreteCategory.hom (TopCat.pullbackIsoProdSubtype f g).inv) x) =
(↑x).2- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.pullbackstatement · cited by 864
- CategoryTheory.Limits.pullback.sndstatement · cited by 637
- CategoryTheory.Limits.WalkingCospanstatement · cited by 496
- CategoryTheory.Limits.cospanstatement · cited by 467
Cited by5
Results whose statement or proof uses this declaration.
- TopCat.pullback_snd_image_fst_preimageproof · cited by 2
- TopCat.GlueData.rel_equivproof · cited by 1
- TopCat.pullback_fst_image_snd_preimageproof · cited by 1
- TopCat.pullback_snd_rangeproof · cited by 1
- factorsThrough_of_pullbackConditionproof · cited by 1