Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.trans_comp

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {X : AlgebraicGeometry.Scheme}
  (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X)
  [inst : CategoryTheory.Category.{v_1, u_1} 𝒰.I₀] [inst_1 : 𝒰.LocallyDirected] {i j k : 𝒰.I₀} (hij : i ⟶ j)
  (hjk : j ⟶ k),
  𝒰.trans (CategoryTheory.CategoryStruct.comp hij hjk) = CategoryTheory.CategoryStruct.comp (𝒰.trans hij) (𝒰.trans hjk)

Defined in: Mathlib.AlgebraicGeometry.Cover.Directed
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category AlgebraicGeometry.Scheme.Cover.LocallyDirected

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites13

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.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
CategoryTheory.PreZeroHypercover.Xstatement · cited by 649
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
AlgebraicGeometry.Scheme.precoveragestatement and proof · cited by 336
AlgebraicGeometry.Scheme.Coverstatement and proof · cited by 88
AlgebraicGeometry.Scheme.Cover.LocallyDirectedstatement and proof · cited by 63
AlgebraicGeometry.Scheme.Cover.transstatement · cited by 43

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_compproof · cited by 0