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<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/abstract>	"In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently from the method chosen for constructing them. For example, the definitions of the integers from the natural numbers, of the rational numbers from the integers, of the real numbers from the rational numbers, and of polynomial rings from the field of their coefficients can all be done in terms of universal properties. In particular, the concept of universal property allows a simple proof that all constructions of real numbers are equivalent: it suffices to prove that they satisfy the same universal property. Technically, a universal property is defined in terms of categories and functors by mean of a universal morphism (see , below). Universal morphisms can also be thought more abstractly as initial or terminal objects of a comma category (see , below). Universal properties occur almost everywhere in mathematics, and the use of the concept allows the use of general properties of universal properties for easily proving some properties that would need boring verifications otherwise. For example, given a commutative ring R, the field of fractions of the quotient ring of R by a prime ideal p can be identified with the residue field of the localization of R at p; that is (all these constructions can be defined by universal properties). Other objects that can be defined by universals properties include: all free objects, direct products and direct sums, free groups, free lattices, Grothendieck group, completion of a metric space, completion of a ring, Dedekind\u2013MacNeille completion, product topologies, Stone\u2013\u010Cech compactification, tensor products, inverse limit and direct limit, kernels and cokernels, quotient groups, quotient vector spaces, and other quotient spaces."@en .
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<http://dbpedia.org/resource/Universal_property>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Dalam teori kategori, cabang dari matematika, sifat universal adalah sifat penting yang dipenuhi oleh morfisme universal (lihat Definisi Formal). Morfisme universal juga dapat dianggap lebih abstrak sebagai dari (lihat Relasi dengan Kategori Koma). Properti universal terjadi hampir di semua tempat dalam matematika, dan karenanya konsep teoretis kategori yang tepat membantu menunjukkan persamaan antara berbagai cabang matematika. Sifat universal dapat digunakan di bidang matematika lain secara implisit, tetapi definisi abstrak dan dipelajari dalam teori kategori."@in .
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<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/abstract>	"\u5728\u6570\u5B66\u7684\u5F88\u591A\u5206\u652F\uFF0C\u7ECF\u5E38\u7528\u201C\u5728\u7ED9\u5B9A\u67D0\u4E9B\u6761\u4EF6\u4E0B\u5B58\u5728\u552F\u4E00\u6001\u5C04\u201D\u8FD9\u79CD\u5F62\u5F0F\u7684\u6027\u8D28\u6765\u5B9A\u4E49\u4E00\u4E9B\u6784\u9020\u3002\u8FD9\u79CD\u6027\u8D28\u7EDF\u79F0\u4E3A\u6CDB\u6027\u8D28\uFF08\u82F1\u8A9E\uFF1AUniversal property\uFF09\uFF0C\u6709\u65F6\u4E5F\u79F0\u4E3A\u4E07\u6709\u6027\u3002\u8303\u7574\u8BBA\u7814\u7A76\u6CDB\u6027\u8D28\u3002 \u4E86\u89E3\u6CDB\u6027\u8D28\u6700\u597D\u5148\u7814\u7A76\u4E00\u4E9B\u4F8B\u5B50\u3002\u5982\uFF1A\u3001\u76F4\u548C\u3001\u81EA\u7531\u7FA4\u3001\u79EF\u62D3\u6251\u3001\u65AF\u901A-\u5207\u8D6B\u7D27\u81F4\u3001\u5F20\u91CF\u79EF\u3001\u3001\u3001\u4E0E\u4E0A\u6838\u3001\u62C9\u56DE\u3001\u63A8\u51FA\u3001\u7B49\u3002"@zh .
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<http://dbpedia.org/resource/Universal_property>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Eine universelle Eigenschaft ist eine Methode der Mathematik, und dort insbesondere der abstrakten Algebra, sich eine gew\u00FCnschte Struktur ohne Angabe einer konkreten Konstruktion zu verschaffen. Dabei wird f\u00FCr Objekte einer bestimmten Kategorie , z. B. die Kategorie der abstrakten Algebren, eine Eigenschaft festgelegt, z. B. dass es von einem Vektorraum eine injektive Abbildung in die Algebra gebe."@de .
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<http://dbpedia.org/resource/Universal_property>	<http://www.w3.org/2000/01/rdf-schema#comment>	"En math\u00E9matiques, et plus pr\u00E9cis\u00E9ment en th\u00E9orie des cat\u00E9gories, une propri\u00E9t\u00E9 universelle est la propri\u00E9t\u00E9 des objets qui sont la solution d'un probl\u00E8me universel pos\u00E9 par un foncteur. De tr\u00E8s nombreux objets classiques des math\u00E9matiques, comme la notion de produit cart\u00E9sien, de groupe quotient, ou de compactifi\u00E9, peuvent \u00EAtre d\u00E9finis comme des solutions de probl\u00E8mes universels."@fr .
<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/abstract>	"Dalam teori kategori, cabang dari matematika, sifat universal adalah sifat penting yang dipenuhi oleh morfisme universal (lihat Definisi Formal). Morfisme universal juga dapat dianggap lebih abstrak sebagai dari (lihat Relasi dengan Kategori Koma). Properti universal terjadi hampir di semua tempat dalam matematika, dan karenanya konsep teoretis kategori yang tepat membantu menunjukkan persamaan antara berbagai cabang matematika. Sifat universal dapat digunakan di bidang matematika lain secara implisit, tetapi definisi abstrak dan dipelajari dalam teori kategori. Artikel ini memberikan perawatan umum tentang sifat universal. Untuk memahami konsepnya, ada baiknya mempelajari beberapa contoh terlebih dahulu, yang jumlahnya banyak: semua , produk langsung dan jumlah langsung, grup bebas, , , , topologi produk, , , limit invers dan limit langsung, dan kokernel, , dan ."@in .
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<http://dbpedia.org/resource/Universal_property>	<http://www.w3.org/2000/01/rdf-schema#comment>	"In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently from the method chosen for constructing them. For example, the definitions of the integers from the natural numbers, of the rational numbers from the integers, of the real numbers from the rational numbers, and of polynomial rings from the field of their coefficients can all be done in terms of universal properties. In particular, the concept of universal property allows a simple proof that all constructions of real numbers are equivalent: it suffices to prove that they satisfy the same universal property."@en .
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<http://dbpedia.org/resource/Universal_property>	<http://xmlns.com/foaf/0.1/topic>	<http://dbpedia.org/resource/Projective_module> .
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<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/abstract>	"Eine universelle Eigenschaft ist eine Methode der Mathematik, und dort insbesondere der abstrakten Algebra, sich eine gew\u00FCnschte Struktur ohne Angabe einer konkreten Konstruktion zu verschaffen. Dabei wird f\u00FCr Objekte einer bestimmten Kategorie , z. B. die Kategorie der abstrakten Algebren, eine Eigenschaft festgelegt, z. B. dass es von einem Vektorraum eine injektive Abbildung in die Algebra gebe. Die Universalkonstruktion besteht nun darin, die Existenz eines \"kleinsten\" Elements der Kategorie zu behaupten, das die Eigenschaft erf\u00FCllt. Im Beispiel w\u00E4re das die Tensoralgebra von . \"Kleinstes\" zu sein bedeutet, dass es zu jedem Objekt der Kategorie , das die geforderte Eigenschaft erf\u00FCllt, einen eindeutig bestimmten Morphismus gibt, der mit der Eigenschaft vertr\u00E4glich ist, im Beispiel mit der Einbettung von vertauscht. Das \"kleinste\" Element muss nicht eindeutig bestimmt sein, jedoch sind alle \"kleinsten\" Elemente, sofern existent, isomorph. Als Existenzbeweis wird meistens eine konkrete Konstruktion angegeben, jedoch sind meistens die Details der Konstruktion f\u00FCr die Theorie der Struktur unwesentlich."@de .
<http://dbpedia.org/resource/Universal_property>	<http://xmlns.com/foaf/0.1/topic>	<http://dbpedia.org/resource/Multiplier_algebra> .
<http://dbpedia.org/resource/Universal_property>	<http://xmlns.com/foaf/0.1/topic>	<http://dbpedia.org/resource/Universal_morphism> .
<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Paul_Cohn> .
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<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Forgetful_functor> .
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<http://dbpedia.org/resource/Universal_property>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Daniel_Kan> .
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<http://dbpedia.org/resource/Universal_property>	<http://xmlns.com/foaf/0.1/topic>	<http://dbpedia.org/resource/Glossary_of_algebraic_geometry> .
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<http://dbpedia.org/resource/Universal_property>	<http://xmlns.com/foaf/0.1/topic>	<http://dbpedia.org/resource/Free_group> .
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<http://dbpedia.org/resource/Universal_property>	<http://xmlns.com/foaf/0.1/topic>	<http://dbpedia.org/resource/Classifying_space> .