Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Pullback.t_id

∀ {X Y Z : AlgebraicGeometry.Scheme} (𝒰 : X.OpenCover) (f : X ⟶ Z) (g : Y ⟶ Z)
  [inst : ∀ (i : 𝒰.I₀), CategoryTheory.Limits.HasPullback (CategoryTheory.CategoryStruct.comp (𝒰.f i) f) g] (i : 𝒰.I₀),
  AlgebraicGeometry.Scheme.Pullback.t 𝒰 f g i i =
    CategoryTheory.CategoryStruct.id (AlgebraicGeometry.Scheme.Pullback.v 𝒰 f g i i)

Defined in: Mathlib.AlgebraicGeometry.Pullbacks
Cited by: 0 results in Mathlib
Foundations: Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Limits.HasPullback

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Cites25

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

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CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
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AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.Limits.pullbackproof · cited by 864
CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
CategoryTheory.PreZeroHypercover.Xstatement and proof · cited by 649
CategoryTheory.Limits.pullback.fstproof · cited by 639
CategoryTheory.Limits.pullback.sndproof · cited by 637
CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542

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AlgebraicGeometry.Scheme.Pullback.gluingproof · cited by 30