Übersetzung für 'category theory' von Englisch nach Deutsch

category theory

Kategorientheorie {f}acad.math.

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category three stadium <category 3 stadium> [UEFA]

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

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

infinity category <∞-category>

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

von Neumann-Bernays-Gödel set theory <NBG set theory>

Neumann-Bernays-Gödel-Mengenlehre {f} <NBG-Mengenlehre>math.

Morse-Kelley set theory <MK set theory>

Morse-Kelley-Mengenlehre {f} <MK-Mengenlehre>math.

Kelley-Morse set theory <KM set theory>

Kelley-Morse-Mengenlehre {f} [selten] [Morse-Kelley-Mengenlehre]math.

Bardeen-Cooper-Schrieffer theory <BCS theory>

Bardeen-Cooper-Schrieffer-Theorie {f} <BCS-Theorie>phys.

molecular orbital theory <MO theory>

Molekülorbitaltheorie {f} <MO-Theorie>chem.

Kaluza-Klein theory <KK theory>

Kaluza-Klein-Theorie {f}phys.

valence bond theory <VB theory>

Valenzstrukturtheorie {f} [auch: VB-Theorie]chem.phys.

Elektronenpaar-Theorie {f} [Valenzstrukturtheorie]chem.phys.

Valenzbindungs­theorie {f} <VB-Theorie>chem.phys.

Tarski-Grothendieck set theory <TG, TG set theory>

Tarski-Grothendieck-Mengenlehre {f} <TG>math.

category

Rubrik {f}

Klasse {f}

Gruppe {f} [Kategorie]

Gattung {f}

Kategorie {f}

Ordnung {f}

• Grothendieck's emphasis on the role of universal properties across varied mathematical structures brought category theory into the mainstream as an organizing principle for mathematics in general.
• "Sets" in the definitions above may be replaced with classes, as is generally the case in category theory.
• In the parlance of category theory, the theorem can be concisely stated by saying that the fundamental group functor takes pushouts (in the category of topological spaces) along inclusions to pushouts (in the category of groups).
• Directed sets also give rise to direct limits in abstract algebra and (more generally) category theory.
• More abstractly, one talks about the product in category theory, which formalizes these notions.

• In the language of category theory, taking the dual of vector spaces and the transpose of linear maps is therefore a contravariant functor from the category of vector spaces over "F" to itself.
• The most general setting in which these words have meaning is an abstract branch of mathematics called category theory.
• The above notions of currying and uncurrying find their most general, abstract statement in category theory.
• In category theory, the cardinal numbers form a skeleton of the category of sets.
• Using the language of category theory, many areas of mathematical study can be categorized. Categories include sets, groups and topologies.

• In category theory, "n"-ary functions generalise to "n"-ary morphisms in a multicategory.
• Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired (as is often the case in category theory).