Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.LocallyDirected.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} [self : 𝒰.LocallyDirected] {i j k : 𝒰.I₀} (hij : i ⟶ j)
(hjk : j ⟶ k),
AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans (CategoryTheory.CategoryStruct.comp hij hjk) =
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans hij)
(AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans hjk)- Defined in
- Mathlib.AlgebraicGeometry.Cover.Directed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · 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.LocallyDirected.transstatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.trans_compproof · cited by 1