Theorems · Theorem · category theory
CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epi
∀ {C : Type u} {X Y : C} [inst : CategoryTheory.Category.{v, u} C] {f g : X ⟶ Y} {c : CategoryTheory.Limits.Fork f g}
(h : CategoryTheory.Limits.IsLimit c) [CategoryTheory.Epi c.ι], CategoryTheory.IsIso c.ιAn equalizer that is an epimorphism is an isomorphism.
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- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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.Cone.ptstatement · cited by 1,298
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
- CategoryTheory.Limits.parallelPairstatement · cited by 766
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.Limits.Fork.ιstatement and proof · cited by 162
- CategoryTheory.Limits.Forkstatement and proof · cited by 85
- CategoryTheory.Limits.Fork.conditionproof · cited by 11
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