Theorems · Theorem · category theory
CategoryTheory.GrothendieckTopology.Point.subsingleton_fiber_obj
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} (Φ : J.Point)
[CategoryTheory.LocallySmall.{w, v, u} C] {U T : C} (f : U ⟶ T) [CategoryTheory.Mono f]
(hT : CategoryTheory.Limits.IsTerminal T), Subsingleton (Φ.fiber.obj U)- Defined in
- Mathlib.CategoryTheory.Sites.Point.Basic
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- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Quiver.Homstatement and proof · cited by 32,603
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- CategoryTheory.Functor.mapproof · cited by 8,698
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- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Monostatement and proof · cited by 893
- Uniqueproof · cited by 400
- CategoryTheory.LocallySmallstatement and proof · cited by 242
- CategoryTheory.Limits.IsTerminalstatement and proof · cited by 153
- CategoryTheory.GrothendieckTopology.Pointstatement and proof · cited by 123
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