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Diff — Sheaf (mathematics)

Revision #1562 → #1847 · back to history

modifiedSheaf of sections of a continuous map2464fa146d0e
FieldFrom #1562To #1847
mathlib.declTopCat.LocalPredicate.isSectionTopCat.isSection
noteThe local predicate `isSection p` produces the sheaf of sections of `p : T → X` via `subsheafToTypes`, but the construction is only set up for trivial fiber families and not the general `Y → X` étalé construction.The local predicate `TopCat.isSection p` produces the sheaf of sections of `p : T → X` via `subsheafToTypes`, but the construction is only set up for trivial fiber families and not the general `Y → X` étalé construction.
modifiedStructure sheaf and differential forms on manifoldsc76bc076e1c9
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mathlib.moduleMathlib.Geometry.Manifold.Sheaf.LocallyRingedSpaceMathlib.Geometry.Manifold.Sheaf.Smooth
modifiedIso/mono check via stalks21cb3976901b
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anchor.sectionMorphismsStalks of a sheaf
anchor.snippetof sheaves oncan be tested on the stalks
labelIso/monomorphism check on open setsIso/mono check via stalks
note`isIso_iff_stalkFunctor_map_iso` and `mono_iff_stalk_mono` reduce iso/mono-ness of a sheaf morphism to stalkwise checks.`isIso_iff_stalkFunctor_map_iso` and `mono_iff_stalk_mono` reduce iso/mono-ness of a sheaf morphism to stalkwise checks; re-anchored from the Morphisms section since the cited decls live in the stalks API.
provenanceaiai-moderated
addedConstant sheafb66a89989f92
addedSchemes as locally ringed spaces48f39145f280
addedSheaf cohomology as derived functor of global sections9c3dd1521d58
addedPullback-pushforward adjunction9568cc09c94b