Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Spec.preimage_comp

∀ {R S T : CommRingCat} (f : AlgebraicGeometry.Spec R ⟶ AlgebraicGeometry.Spec S)
  (g : AlgebraicGeometry.Spec S ⟶ AlgebraicGeometry.Spec T),
  AlgebraicGeometry.Spec.preimage (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.preimage g) (AlgebraicGeometry.Spec.preimage f)

Defined in: Mathlib.AlgebraicGeometry.GammaSpecAdjunction
Cited by: 2 results in Mathlib
Foundations: Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites9

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
AlgebraicGeometry.Schemestatement · cited by 2,540
CommRingCatstatement and proof · cited by 2,333
AlgebraicGeometry.Specstatement and proof · cited by 626
AlgebraicGeometry.Spec.map_compproof · cited by 33
AlgebraicGeometry.Spec.preimagestatement and proof · cited by 14
AlgebraicGeometry.Spec.map_preimageproof · cited by 11
AlgebraicGeometry.Spec.map_injectiveproof · cited by 9

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.eq_bot_of_comp_quotientMk_eq_sigmaSpecproof · cited by 1
AlgebraicGeometry.Spec.preimage_comp_assocproof · cited by 0