Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.appLE_map
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {U : Y.Opens} {V V' : X.Opens}
(e : V ≤ (TopologicalSpace.Opens.map f.base).obj U) (i : Opposite.op V ⟶ Opposite.op V'),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.appLE f U V e) (X.presheaf.map i) =
AlgebraicGeometry.Scheme.Hom.appLE f U V' ⋯- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.Category.assocproof · cited by 6,433
- TopCat.carrierstatement · cited by 3,184
- LE.le.transstatement and proof · cited by 3,151
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- Opposite.unopstatement · cited by 2,231
- TopologicalSpace.Opensstatement · cited by 2,040
Cited by27
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
- AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
- AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturalityproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.appLE_map_assocproof · cited by 4
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
- AlgebraicGeometry.Proj.awayι_comp_mapproof · cited by 3
- AlgebraicGeometry.morphismRestrict_appLEproof · cited by 3
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.exists_app_map_eq_zero_of_isLimitproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.mono_pushoutSection_of_iSup_eqproof · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2