Theorems · Theorem · category theory
CategoryTheory.IsPullback.of_horiz_isIso_mono
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P X Y Z : C} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z}
{g : Y ⟶ Z} [CategoryTheory.IsIso fst] [CategoryTheory.Mono g],
CategoryTheory.CommSq fst snd f g → CategoryTheory.IsPullback fst snd f g- Cited by
- 4 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.invproof · cited by 467
- CategoryTheory.cancel_monoproof · cited by 435
- CategoryTheory.IsPullbackstatement · cited by 320
- CategoryTheory.CommSqstatement and proof · cited by 158
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.IsPullback.of_horiz_isIsoproof · cited by 9
- CategoryTheory.IsPullback.of_vert_isIso_monoproof · cited by 2
- CategoryTheory.Sheaf.isPullback_χ_truthproof · cited by 0
- CategoryTheory.Sheaf.χ_uniqueproof · cited by 0