Theorems · Theorem · category theory
CategoryTheory.GrothendieckTopology.Point.comap_fiber
∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] {K : CategoryTheory.GrothendieckTopology D} (Φ : K.Point)
(F : CategoryTheory.Functor C D) [inst_2 : CategoryTheory.RepresentablyFlat F]
{J : CategoryTheory.GrothendieckTopology C} (hF : CategoryTheory.CoverPreserving J K F)
[inst_3 : CategoryTheory.InitiallySmall (F.comp Φ.fiber).Elements], (Φ.comap F hF).fiber = F.comp Φ.fiber- Defined in
- Mathlib.CategoryTheory.Sites.Point.Comap
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Functor.Elementsstatement and proof · cited by 141
- CategoryTheory.GrothendieckTopology.Pointstatement and proof · cited by 123
- CategoryTheory.GrothendieckTopology.Point.fiberstatement and proof · cited by 93
- CategoryTheory.InitiallySmallstatement and proof · cited by 51
- CategoryTheory.CoverPreservingstatement and proof · cited by 32
- CategoryTheory.RepresentablyFlatstatement and proof · cited by 18
- CategoryTheory.GrothendieckTopology.Point.comapstatement and proof · cited by 3
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