Theorems · Theorem · category theory
CategoryTheory.regularTopology.isSheaf_yoneda_obj
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preregular C] (W : C),
CategoryTheory.Presieve.IsSheaf (CategoryTheory.regularTopology C) (CategoryTheory.yoneda.obj W)Every Yoneda-presheaf is a sheaf for the regular topology.
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- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.GrothendieckTopologyproof · cited by 1,415
- CategoryTheory.Limits.IsColimitproof · cited by 773
- CategoryTheory.Sieveproof · cited by 552
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.Sieve.arrowsproof · cited by 446
- CategoryTheory.yonedastatement and proof · cited by 351
- Nonempty.someproof · cited by 340
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