In mathematics, the constant sheaf on a topological space associated to a set is a sheaf of sets on whose stalks are all equal to . It is denoted by or . The constant presheaf with value is the presheaf that assigns to each non-empty open subset of the value , and all of whose restriction maps are the identity map . The constant sheaf associated to is the sheafification of the constant presheaf associated to . This sheaf identifies with the sheaf of locally constant -valued functions on . Constant sheaves of abelian groups appear in particular as coefficients in sheaf cohomology.
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| rdfs:label
| - Constant sheaf (en)
- Haz constante (es)
- 상수층 (ko)
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| - 층 이론에서, 상수층(常數層, 영어: constant sheaf)은 모든 줄기가 같은 층이다. (ko)
- In mathematics, the constant sheaf on a topological space associated to a set is a sheaf of sets on whose stalks are all equal to . It is denoted by or . The constant presheaf with value is the presheaf that assigns to each non-empty open subset of the value , and all of whose restriction maps are the identity map . The constant sheaf associated to is the sheafification of the constant presheaf associated to . This sheaf identifies with the sheaf of locally constant -valued functions on . Constant sheaves of abelian groups appear in particular as coefficients in sheaf cohomology. (en)
- En matemáticas el haz constante en un espacio topológico X asociado al conjunto A es un haz de conjuntos en X cuyos tallos son todos iguales a A. Este es denotado A o AX. El prehaz constante con valores en A es el prehaz que asigna a cada subconjunto no vacío de X el valor A, y todos los mapeos de restricción son la identidad A → A. El haz constante asociado a A es el del prehaz constante asociado a A. En ciertos casos, el conjunto A puede ser reemplazado con un objeto A en alguna categoría C (por ejemplo cuando C es la categoría de los grupos abelianos, o de los anillos conmutativos). (es)
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| - In mathematics, the constant sheaf on a topological space associated to a set is a sheaf of sets on whose stalks are all equal to . It is denoted by or . The constant presheaf with value is the presheaf that assigns to each non-empty open subset of the value , and all of whose restriction maps are the identity map . The constant sheaf associated to is the sheafification of the constant presheaf associated to . This sheaf identifies with the sheaf of locally constant -valued functions on . In certain cases, the set may be replaced with an object in some category (e.g. when is the category of abelian groups, or commutative rings). Constant sheaves of abelian groups appear in particular as coefficients in sheaf cohomology. (en)
- En matemáticas el haz constante en un espacio topológico X asociado al conjunto A es un haz de conjuntos en X cuyos tallos son todos iguales a A. Este es denotado A o AX. El prehaz constante con valores en A es el prehaz que asigna a cada subconjunto no vacío de X el valor A, y todos los mapeos de restricción son la identidad A → A. El haz constante asociado a A es el del prehaz constante asociado a A. En ciertos casos, el conjunto A puede ser reemplazado con un objeto A en alguna categoría C (por ejemplo cuando C es la categoría de los grupos abelianos, o de los anillos conmutativos). El haz constante de grupos abielianos aparece en particular como coeficientes en la cohomología de haces.
* Datos: Q5163667 (es)
- 층 이론에서, 상수층(常數層, 영어: constant sheaf)은 모든 줄기가 같은 층이다. (ko)
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