Theorems · Theorem · category theory
CategoryTheory.adhesive_of_preserves_and_reflects_isomorphism
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u''} [inst_1 : CategoryTheory.Category.{v'', u''} D]
(F : CategoryTheory.Functor C D) [CategoryTheory.Adhesive D] [CategoryTheory.Limits.HasPullbacks C]
[CategoryTheory.Limits.HasPushouts C]
[CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingCospan F]
[CategoryTheory.Limits.PreservesColimitsOfShape CategoryTheory.Limits.WalkingSpan F] [F.ReflectsIsomorphisms],
CategoryTheory.Adhesive C- Defined in
- Mathlib.CategoryTheory.Adhesive.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.WalkingCospanstatement and proof · cited by 496
- CategoryTheory.Limits.HasPullbacksstatement and proof · cited by 439
- CategoryTheory.Limits.WalkingSpanstatement and proof · cited by 300
- CategoryTheory.Limits.PreservesColimitsOfShapestatement and proof · cited by 222
- CategoryTheory.Limits.HasPushoutsstatement and proof · cited by 172
- CategoryTheory.Limits.PreservesLimitsOfShapestatement and proof · cited by 156
- CategoryTheory.Functor.ReflectsIsomorphismsstatement and proof · cited by 82
- CategoryTheory.Limits.ReflectsColimitsOfShapeproof · cited by 30
- CategoryTheory.Limits.ReflectsLimitsOfShapeproof · cited by 30
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