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Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Cover.shape

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} → {J : CategoryTheory.GrothendieckTopology C} → J.Cover X → CategoryTheory.Limits.MulticospanShape

The shape of the multiequalizer diagrams associated to S : J.Cover X.

Defined in
Mathlib.CategoryTheory.Sites.Grothendieck
Cited by
147 results in Mathlib
Foundations
Depth 35 from the axioms, rests on 233 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.GrothendieckTopology.Cover.index · cited by 142Cover.indexCategoryTheory.GrothendieckTopology.plusObj · cited by 56GrothendieckTopology.plus…CategoryTheory.GrothendieckTopology.sheafify · cited by 32GrothendieckTopology.shea…CategoryTheory.GrothendieckTopology.diagram · cited by 29GrothendieckTopology.diag…CategoryTheory.GrothendieckTopology.toPlus · cited by 28GrothendieckTopology.toPl…CategoryTheory.GrothendieckTopology.plusMap · cited by 26GrothendieckTopology.plus…CategoryTheory.GrothendieckTopology.plusCompIso · cited by 20GrothendieckTopology.plus…CategoryTheory.GrothendieckTopology.toSheafify · cited by 19GrothendieckTopology.toSh…CategoryTheory.GrothendieckTopology.diagramNatTrans · cited by 12GrothendieckTopology.diag…CategoryTheory.GrothendieckTopology.sheafifyCompIso · cited by 11GrothendieckTopology.shea…CategoryTheory.GrothendieckTopology.plusLift · cited by 10GrothendieckTopology.plus…CategoryTheory.GrothendieckTopology.sheafifyLift · cited by 9GrothendieckTopology.shea…CategoryTheory.GrothendieckTopology.Plus.mk · cited by 9Plus.mkCategoryTheory.Meq.equiv · cited by 8Meq.equivCategoryTheory.GrothendieckTopology.plusFunctor · cited by 8GrothendieckTopology.plus…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.GrothendieckTopology.Cover · cited by 211GrothendieckTopology.CoverCategoryTheory.Limits.MulticospanShape · cited by 160Limits.MulticospanShapeCategoryTheory.GrothendieckTopology.Cover.Arrow · cited by 99Cover.ArrowCategoryTheory.GrothendieckTopology.Cover.Relation · cited by 25Cover.RelationCategoryTheory.GrothendieckTopology.Cover.Relation.fst · cited by 22Relation.fstCategoryTheory.GrothendieckTopology.Cover.Relation.snd · cited by 22Relation.sndCover.shapeCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by217

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 217.