Theorems · Theorem · category theory
CategoryTheory.Limits.PullbackCone.isIso_fst_of_mono_of_isLimit
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y} [CategoryTheory.Mono f]
{t : CategoryTheory.Limits.PullbackCone f f} (ht : CategoryTheory.Limits.IsLimit t), CategoryTheory.IsIso t.fst- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.PullbackCone.isIso_snd_of_mono_of_isLimitproof · cited by 1
- CategoryTheory.IsPullback.isIso_fst_of_monoproof · cited by 1