Übersetzung für 'abelian category' von Englisch nach Deutsch

abelian category

abelsche Kategorie {f}math.

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Abelian {adj}

abelschmath.

kommutativmath.

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category five stadium <category 5 stadium> [UEFA]

Fünf-Sterne-Stadion {n} <5-Sterne-Stadion> [UEFA]sports

category four stadium <category 4 stadium> [UEFA]

Vier-Sterne-Stadion {n} <4-Sterne-Stadion> [UEFA]sports

category three stadium <category 3 stadium> [UEFA]

Drei-Sterne-Stadion {n} <3-Sterne-Stadion> [UEFA]sports

abelian variety

abelsche Varietät {f}math.

non-abelian {adj}

nicht-abelschmath.

abelian Lie algebra

abelsche Lie-Algebra {f}math.

free abelian group

freie abelsche Gruppe {f}math.

infinity category <∞-category>

Unendlich-Kategorie {f} <∞-Kategorie>math.

Abelian group [also: abelian group]

Abel'sche Gruppe {f}math.

Abelsche Gruppe {f} [alt]math.

abelsche Gruppe {f}math.

Abelian extension [also: abelian extension]

abelsche Erweiterung {f}math.

(main) theorem about finite Abelian groups

Hauptsatz {m} über endlich erzeugte abelsche Gruppenmath.

non-Abelian group [also: non-abelian group]

nichtabelsche Gruppe {f} [auch: nicht-abelsche Gruppe]math.

category

Kategorie {f}

Ordnung {f}

Klasse {f}

Gruppe {f} [Kategorie]

• His notion of abelian category is now the basic object of study in homological algebra.
• Of course, if the abelian category is the category of coherent sheaves on a scheme, then this construction can be used to form a presheaf of groupoids.
• Originally, the "Grothendieck group" was, more specifically, the result of this construction applied to the equivalences classes under isomorphisms of the objects of an abelian category, with the direct sum as semigroup operation.
• The finitely generated abelian groups, together with the group homomorphisms, form an abelian category which is a Serre subcategory of the category of abelian groups.
• The category Ab, consisting of all abelian groups and their group homomorphisms, is a full subcategory of Grp, and the prototype of an abelian category.

• This applies to the "I"-indexed diagrams in the category of "R"-modules, with "R" a commutative ring; it is not necessarily true in an arbitrary abelian category (see Roos' "Derived functors of inverse limits revisited" for examples of abelian categories in which lim"n", on diagrams indexed by a countable set, is nonzero for "n" > 1).
• The above compatibility also shows that the category of all abelian groups with group homomorphisms forms a preadditive category; the existence of direct sums and well-behaved kernels makes this category the prototypical example of an abelian category.
• The preadditive categories most commonly studied are in fact abelian categories; for example, Ab is an abelian category.
• The collection of all abelian groups, together with the homomorphisms between them, forms the category [...] , the prototype of an abelian category.