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sheaf (Definition)

"sheaf" is owned by djao.
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See Also: stalk, prime spectrum, sheafification, sheaf

Also defines:  presheaf, section, morphism of sheaves, isomorphism of sheaves, sheaf isomorphism

Attachments:
presheaf of a topological basis (Definition) by jocaps
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Cross-references: varieties, algebraic, property, branches, language, power, connected, cover, constant functions, scope, commutative ring, prime spectrum, complex, holomorphic functions, complex analytic manifold, schemes, algebraic structures, coordinate, algebraic geometry, field, force, differential geometry, structure, sufficient, smooth functions, second countable, locally Euclidean, vector spaces, real, differentiable manifold, smooth, subset, rings, obvious, subcategory, even, group, difference, abelian group, similar, factor, onto, projection, universal properties, categorical direct product, induce, exact sequence, sequence, abelian category, open cover, concrete category, inverse morphism, homeomorphism, composition, isomorphism, map, identity map, natural transformation, collection, presheaves, continuous map, identity, restriction, equivalent, inclusion mappings, morphisms, open sets, objects, contravariant functor, category, topological space
There are 53 references to this entry.

This is version 11 of sheaf, born on 2002-04-28, modified 2006-11-30.
Object id is 2878, canonical name is Sheaf.
Accessed 14708 times total.

Classification:
AMS MSC18F20 (Category theory; homological algebra :: Categories and geometry :: Presheaves and sheaves)
 54B40 (General topology :: Basic constructions :: Presheaves and sheaves)
 14F05 (Algebraic geometry :: homology theory :: Vector bundles, sheaves, related constructions)

Pending Errata and Addenda
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Discussion
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Sheaf on a site by archibal on 2004-02-26 02:15:30
I want to write an entry on the notion of sheaves on a site. Is it better to put it in with the (already long) entry on sheaves on a topological space, or in its own entry? It's really a direct generalization.

Similar issues arise with sheafification, although in this case there is the possibility of set-theoretic difficulties.
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