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Theorems · Definition · algebraic geometry

AlgebraicGeometry.coprodIsoSigma

(X Y : AlgebraicGeometry.Scheme) → X ⨿ Y ≅ ∐ fun i => CategoryTheory.Limits.WalkingPair.casesOn i.down X Y

(Implementation Detail) The coproduct of the two schemes is given by indexed coproducts over WalkingPair.

Defined in
Mathlib.AlgebraicGeometry.Limits
Cited by
2 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.ι_left_coprodIsoSigma_inv · cited by 0AlgebraicGeometry.ι_left_…AlgebraicGeometry.ι_right_coprodIsoSigma_inv · cited by 0AlgebraicGeometry.ι_right…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso · cited by 3963CategoryTheory.IsoEquiv.symm · cited by 3681Equiv.symmAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Discrete.functor · cited by 633Discrete.functorCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.sigmaObj · cited by 302Limits.sigmaObjCategoryTheory.Limits.coprod · cited by 252Limits.coprodAlgebraicGeometry.coprodIsoSi…CITED BYCITES

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