Theorems · Theorem · category theory
CategoryTheory.extensiveTopology.isSheaf_yoneda_obj
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.FinitaryPreExtensive C] (W : C),
CategoryTheory.Presieve.IsSheaf (CategoryTheory.extensiveTopology C) (CategoryTheory.yoneda.obj W)Every Yoneda-presheaf is a sheaf for the extensive topology.
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- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites25
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement · cited by 8,081
- Finiteproof · cited by 3,029
- CategoryTheory.GrothendieckTopologyproof · cited by 1,415
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.yonedastatement and proof · cited by 351
- CategoryTheory.Precoverage.coveringsproof · cited by 194
- CategoryTheory.Limits.Cofan.injproof · cited by 170
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