Theorems · Definition · algebraic geometry
AlgebraicGeometry.SheafedSpace.forgetToPresheafedSpace
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
CategoryTheory.Functor (AlgebraicGeometry.SheafedSpace C) (AlgebraicGeometry.PresheafedSpace C)Forgetting the sheaf condition is a functor from SheafedSpace C to PresheafedSpace C.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CategoryTheory.Functorstatement · cited by 16,252
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.PresheafedSpacestatement · cited by 260
- AlgebraicGeometry.SheafedSpacestatement · cited by 142
- CategoryTheory.inducedFunctorproof · cited by 14
Cited by31
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.SheafedSpace.Γproof · cited by 6
- AlgebraicGeometry.Spec.toPresheafedSpaceproof · cited by 5
- AlgebraicGeometry.SheafedSpace.GlueData.toPresheafedSpaceGlueDataproof · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eqstatement · cited by 3
- AlgebraicGeometry.Scheme.GlueData.isoCarrierproof · cited by 3
- AlgebraicGeometry.Scheme.GlueData.ι_eq_iffproof · cited by 2
- AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_invproof · cited by 2
- AlgebraicGeometry.SheafedSpace.GlueData.isoPresheafedSpaceproof · cited by 2
- AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_appstatement · cited by 1
- AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app'statement · cited by 1
- AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_invproof · cited by 1