Theorems · Definition · algebraic geometry
AlgebraicGeometry.coprodMk
(X Y : AlgebraicGeometry.Scheme) → ↥X ⊕ ↥Y ≃ₜ ↥(X ⨿ Y)
The underlying topological space of the coproduct is homeomorphic to the disjoint union
- Defined in
- Mathlib.AlgebraicGeometry.Limits
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Functor.compstatement · cited by 6,529
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Discretestatement · cited by 2,447
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.coprodMk_inlstatement · cited by 3
- AlgebraicGeometry.coprodMk_inrstatement · cited by 3
- AlgebraicGeometry.isPullback_inl_inl_coprodMapproof · cited by 2
- AlgebraicGeometry.coprodSpec_coprodMkstatement · cited by 1
- AlgebraicGeometry.coprodSpec_applystatement and proof · cited by 0
- AlgebraicGeometry.isIso_stalkMap_coprodSpecproof · cited by 0