. . "\u5728\u7BC4\u7587\u8AD6\u4E2D\uFF0C\u51FD\u5B50\u82E5\u6EFF\u8DB3\uFF0C\u5247\u7A31\u4E4B\u70BA\u4E00\u5C0D\u4F34\u96A8\u51FD\u5B50\uFF0C\u5176\u4E2D\u7A31\u70BA\u7684\u53F3\u4F34\u96A8\u51FD\u5B50\uFF0C\u800C\u662F\u7684\u5DE6\u4F34\u96A8\u51FD\u5B50\u3002\u4F34\u96A8\u51FD\u5B50\u5728\u7BC4\u7587\u8AD6\u4E2D\u662F\u500B\u6975\u57FA\u672C\u800C\u6709\u7528\u7684\u6982\u5FF5\u3002"@zh . "Adjunktion ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie.Zwei Funktoren und zwischen Kategorien und hei\u00DFen adjungiert, wenn sie eine gewisse Beziehung zwischen Morphismenmengen vermitteln. Dieser Begriff wurde von D. M. Kan eingef\u00FChrt."@de . . . . "Foncteur adjoint"@fr . . . "\u0421\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u0435 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B \u2014 \u043F\u0430\u0440\u0430 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u043E\u0432, \u0441\u043E\u0441\u0442\u043E\u044F\u0449\u0438\u0445 \u0432 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u043E\u043C \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0438 \u043C\u0435\u0436\u0434\u0443 \u0441\u043E\u0431\u043E\u0439. \u0421\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u0435 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B \u0447\u0430\u0441\u0442\u043E \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044E\u0442\u0441\u044F \u0432 \u0440\u0430\u0437\u043D\u044B\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438. \u041D\u0435\u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E, \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B F \u0438 G \u0441\u043E\u043F\u0440\u044F\u0436\u0435\u043D\u044B, \u0435\u0441\u043B\u0438 \u043E\u043D\u0438 \u0443\u0434\u043E\u0432\u043B\u0435\u0442\u0432\u043E\u0440\u044F\u044E\u0442 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044E . \u0422\u043E\u0433\u0434\u0430 F \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043B\u0435\u0432\u044B\u043C \u0441\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u043C \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u043E\u043C, \u0430 G \u2014 \u043F\u0440\u0430\u0432\u044B\u043C."@ru . . . . . . . . . . . "\u0421\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u0435 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B"@ru . "\u6570\u5B66\u306E\u7279\u306B\u570F\u8AD6\u306B\u304A\u3051\u308B\u968F\u4F34\uFF08\u305A\u3044\u306F\u3093\u3001\u82F1: adjunction\uFF09\u306F\u3001\u4E8C\u3064\u306E\u95A2\u624B\u306E\u9593\u306B\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\uFF08\u3042\u308B\u7A2E\u306E\u53CC\u5BFE\u7684\u306A\uFF09\u95A2\u4FC2\u3092\u3044\u3046\u3002\u968F\u4F34\u306E\u6982\u5FF5\u306F\u6570\u5B66\u306B\u904D\u5728\u3057\u3001\u6700\u9069\u5316\u3084\u52B9\u7387\u306B\u95A2\u3059\u308B\u76F4\u89B3\u7684\u6982\u5FF5\u3092\u660E\u3089\u304B\u306B\u3059\u308B\u3002 \u6700\u3082\u7C21\u6F54\u306A\u5BFE\u79F0\u7684\u5B9A\u7FA9\u306B\u304A\u3044\u3066\u3001\u570F \U0001D49E \u3068 \U0001D49F \u306E\u9593\u306E\u968F\u4F34\u3068\u306F\u3001\u4E8C\u3064\u306E\u95A2\u624B \u306E\u5BFE\u3067\u3042\u3063\u3066\u3001\u5168\u5358\u5C04\u306E\u65CF \u304C\u5909\u6570 X, Y \u306B\u95A2\u3057\u3066\u81EA\u7136\uFF08\u3042\u308B\u3044\u306F\u51FD\u624B\u7684\uFF09\u3068\u306A\u308B\u3082\u306E\u3092\u8A00\u3046\u3002\u3053\u306E\u3068\u304D\u3001\u95A2\u624B F \u3092\u5DE6\u968F\u4F34\u51FD\u624B\u3068\u547C\u3073\u3001\u4ED6\u65B9 G \u3092\u53F3\u968F\u4F34\u51FD\u624B\u3068\u547C\u3076\u3002\u307E\u305F\u3001\u300CF \u306F G \u306E\u5DE6\u968F\u4F34\u3067\u3042\u308B\u300D (\u540C\u3058\u3053\u3068\u3060\u304C\u3001\u300CG \u306F F \u306E\u53F3\u968F\u4F34\u3067\u3042\u308B\u300D)\u3068\u3044\u3046\u95A2\u4FC2\u3092 \u3068\u66F8\u304F\u3002 \u4EE5\u4E0B\u3067\u306F\u3001\u3053\u306E\u5B9A\u7FA9\u3084\u4ED6\u306E\u5B9A\u7FA9\u3092\u8A73\u7D30\u5316\u3059\u308B\u3002"@ja . . . . "\u4F34\u96A8\u51FD\u5B50"@zh . . . . "\uBC94\uC8FC\uB860\uC5D0\uC11C \uC218\uBC18 \uD568\uC790(\u96A8\u4F34\u51FD\u5B50, \uC601\uC5B4: adjoint functor) \uB610\uB294 \uB538\uB9BC \uD568\uC790(-\u51FD\u5B50)\uB294 \uB450 \uAC1C\uC758 \uD568\uC790\uAC00 \uC11C\uB85C\uAC04\uC5D0 \uAC00\uC9C8 \uC218 \uC788\uB294 \uC77C\uC885\uC758 \uBC00\uC811\uD55C \uAD00\uACC4\uC774\uB2E4. \uC774\uB294 \uC218\uD559\uC758 \uB9CE\uC740 \uBD84\uC57C\uC5D0\uC11C \uB110\uB9AC \uB098\uD0C0\uB098\uB294 \uAD00\uACC4\uC774\uBA70, \uBC94\uC8FC\uB860\uC758 \uC5F0\uAD6C \uB300\uC0C1\uC774\uB2E4."@ko . . . . . . . . . . . . "L'adjonction est une situation omnipr\u00E9sente en math\u00E9matiques, et formalis\u00E9e en th\u00E9orie des cat\u00E9gories par la notion de foncteurs adjoints. Une adjonction entre deux cat\u00E9gories et est une paire de deux foncteurs et v\u00E9rifiant que, pour tout objet X dans C et Y dans D, il existe une bijection entre les ensembles de morphismes correspondants et la famille de bijections est naturelle en X et Y. On dit que F et G sont des foncteurs adjoints et plus pr\u00E9cis\u00E9ment, que F est \u00AB adjoint \u00E0 gauche de G \u00BB ou que G est \u00AB adjoint \u00E0 droite de F \u00BB."@fr . . . . . "Adjunktion ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie.Zwei Funktoren und zwischen Kategorien und hei\u00DFen adjungiert, wenn sie eine gewisse Beziehung zwischen Morphismenmengen vermitteln. Dieser Begriff wurde von D. M. Kan eingef\u00FChrt."@de . . . . . . . . . . "Funtore aggiunto"@it . . "Funktory sprz\u0119\u017Cone \u2013 jedno z centralnych poj\u0119\u0107 zaawansowanej teorii kategorii, \u015Bci\u015Ble zwi\u0105zane z innymi wa\u017Cnymi poj\u0119ciami, w szczeg\u00F3lno\u015Bci z rozmaitymi zagadnieniami jednoznacznej faktoryzacji oraz z funktorami reprezentowalnymi poprzez funktory g\u0142\u00F3wne (zwane te\u017C hom-funktorami). W przeciwie\u0144stwie do wielu innych poj\u0119\u0107 teorii kategorii, kt\u00F3re mo\u017Cna uzna\u0107 za wys\u0142owienie w j\u0119zyku kategorii intuicji oswojonych ju\u017C w ramach algebry lub topologii, poj\u0119cie funktora sprz\u0119\u017Conego jest istotnie nowe."@pl . . "Funktory sprz\u0119\u017Cone"@pl . "En matem\u00E1ticas, espec\u00EDficamente en teor\u00EDa de categor\u00EDas, la adjunci\u00F3n es una relaci\u00F3n entre dos funtores que aparece frecuentemente a trav\u00E9s de las distintas ramas de las matem\u00E1ticas y que captura una noci\u00F3n intuitiva de soluci\u00F3n a un problema de optimizaci\u00F3n. Dos funtores y se dicen adjuntos entre s\u00ED, si existe una familia de biyecciones que es natural para cualesquiera e . La relaci\u00F3n de que sea adjunto a izquierda de , o, equivalentemente, que sea adjunto a derecha de , se nota como ."@es . . . . . . . . . . . "1118292486"^^ . . . "Funktory sprz\u0119\u017Cone \u2013 jedno z centralnych poj\u0119\u0107 zaawansowanej teorii kategorii, \u015Bci\u015Ble zwi\u0105zane z innymi wa\u017Cnymi poj\u0119ciami, w szczeg\u00F3lno\u015Bci z rozmaitymi zagadnieniami jednoznacznej faktoryzacji oraz z funktorami reprezentowalnymi poprzez funktory g\u0142\u00F3wne (zwane te\u017C hom-funktorami). W przeciwie\u0144stwie do wielu innych poj\u0119\u0107 teorii kategorii, kt\u00F3re mo\u017Cna uzna\u0107 za wys\u0142owienie w j\u0119zyku kategorii intuicji oswojonych ju\u017C w ramach algebry lub topologii, poj\u0119cie funktora sprz\u0119\u017Conego jest istotnie nowe."@pl . . . . . . . . . . . . . . . "Na teoria das categorias, uma adjun\u00E7\u00E3o \u00E9 uma tripla consistindo de dois functores , e uma fam\u00EDlia de isomorfismos natural em ; a condi\u00E7\u00E3o de naturalidade \u00E9 expressa por para cada , e , ou equivalentemente por para cada , e . Nesse caso, \u00E9 dito adjunto esquerdo a , e \u00E9 dito adjunto direito a , e escreve-se . Segundo Saunders Mac Lane, \"functores adjuntos s\u00E3o onipresentes\". Com efeito, v\u00E1rios conceitos da matem\u00E1tica, como grupos livres, corpo de quocientes e completa\u00E7\u00E3o de espa\u00E7os m\u00E9tricos s\u00E3o casos particulares do conceito de adjun\u00E7\u00E3o."@pt . . "Adjunktion (Kategorientheorie)"@de . . . . . . . . . . . . . . . . . "In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of \"optimal solutions\" to certain problems (i.e., constructions of objects having a certain universal property), such as the construction of a free group on a set in algebra, or the construction of the Stone\u2013\u010Cech compactification of a topological space in topology. By definition, an adjunction between categories and is a pair of functors (assumed to be covariant) and and, for all objects in and in a bijection between the respective morphism sets such that this family of bijections is natural in and . Naturality here means that there are natural isomorphisms between the pair of functors and for a fixed in , and also the pair of functors and for a fixed in . The functor is called a left adjoint functor or left adjoint to , while is called a right adjoint functor or right adjoint to . An adjunction between categories and is somewhat akin to a \"weak form\" of an equivalence between and , and indeed every equivalence is an adjunction. In many situations, an adjunction can be \"upgraded\" to an equivalence, by a suitable natural modification of the involved categories and functors."@en . . . . . "Adjun\u00E7\u00E3o (teoria das categorias)"@pt . . "Adjoint functors"@en . . . . "\u0421\u043F\u0440\u044F\u0436\u0435\u043D\u0456 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438"@uk . . . . "Adjunkce je v teorii kategori\u00ED vztah mezi dv\u011Bma funktory (a t\u00EDm i vztah mezi dv\u011Bma kategoriemi), kter\u00E9 se ozna\u010Duj\u00ED jako adjungovan\u00E9 funktory, co\u017E se zna\u010D\u00ED jako , p\u0159i\u010Dem\u017E je adjungovan\u00FD zleva ke (a naopak je adjungovan\u00FD zprava k ). M\u00E1me-li funktory a , pak je , pokud pro ka\u017Ed\u00E9 a existuje bijekce p\u0159irozen\u00E1 v obou parametrech. Existence adjungovan\u00FDch funktor\u016F mezi dv\u011Bma kategoriemi vyjad\u0159uje m\u00EDrn\u011Bj\u0161\u00ED obdobu ekvivalence t\u011Bchto kategori\u00ED."@cs . . . . . . "53991"^^ . . . . . . . . . . . . . . "L'adjonction est une situation omnipr\u00E9sente en math\u00E9matiques, et formalis\u00E9e en th\u00E9orie des cat\u00E9gories par la notion de foncteurs adjoints. Une adjonction entre deux cat\u00E9gories et est une paire de deux foncteurs et v\u00E9rifiant que, pour tout objet X dans C et Y dans D, il existe une bijection entre les ensembles de morphismes correspondants et la famille de bijections est naturelle en X et Y. On dit que F et G sont des foncteurs adjoints et plus pr\u00E9cis\u00E9ment, que F est \u00AB adjoint \u00E0 gauche de G \u00BB ou que G est \u00AB adjoint \u00E0 droite de F \u00BB."@fr . . . . . . "\uBC94\uC8FC\uB860\uC5D0\uC11C \uC218\uBC18 \uD568\uC790(\u96A8\u4F34\u51FD\u5B50, \uC601\uC5B4: adjoint functor) \uB610\uB294 \uB538\uB9BC \uD568\uC790(-\u51FD\u5B50)\uB294 \uB450 \uAC1C\uC758 \uD568\uC790\uAC00 \uC11C\uB85C\uAC04\uC5D0 \uAC00\uC9C8 \uC218 \uC788\uB294 \uC77C\uC885\uC758 \uBC00\uC811\uD55C \uAD00\uACC4\uC774\uB2E4. \uC774\uB294 \uC218\uD559\uC758 \uB9CE\uC740 \uBD84\uC57C\uC5D0\uC11C \uB110\uB9AC \uB098\uD0C0\uB098\uB294 \uAD00\uACC4\uC774\uBA70, \uBC94\uC8FC\uB860\uC758 \uC5F0\uAD6C \uB300\uC0C1\uC774\uB2E4."@ko . . . . . . . . . . . . . . "\u0421\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u0435 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B \u2014 \u043F\u0430\u0440\u0430 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u043E\u0432, \u0441\u043E\u0441\u0442\u043E\u044F\u0449\u0438\u0445 \u0432 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u043E\u043C \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0438 \u043C\u0435\u0436\u0434\u0443 \u0441\u043E\u0431\u043E\u0439. \u0421\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u0435 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B \u0447\u0430\u0441\u0442\u043E \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044E\u0442\u0441\u044F \u0432 \u0440\u0430\u0437\u043D\u044B\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438. \u041D\u0435\u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E, \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u044B F \u0438 G \u0441\u043E\u043F\u0440\u044F\u0436\u0435\u043D\u044B, \u0435\u0441\u043B\u0438 \u043E\u043D\u0438 \u0443\u0434\u043E\u0432\u043B\u0435\u0442\u0432\u043E\u0440\u044F\u044E\u0442 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044E . \u0422\u043E\u0433\u0434\u0430 F \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043B\u0435\u0432\u044B\u043C \u0441\u043E\u043F\u0440\u044F\u0436\u0451\u043D\u043D\u044B\u043C \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u043E\u043C, \u0430 G \u2014 \u043F\u0440\u0430\u0432\u044B\u043C."@ru . . "\uC218\uBC18 \uD568\uC790"@ko . . "\u6570\u5B66\u306E\u7279\u306B\u570F\u8AD6\u306B\u304A\u3051\u308B\u968F\u4F34\uFF08\u305A\u3044\u306F\u3093\u3001\u82F1: adjunction\uFF09\u306F\u3001\u4E8C\u3064\u306E\u95A2\u624B\u306E\u9593\u306B\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\uFF08\u3042\u308B\u7A2E\u306E\u53CC\u5BFE\u7684\u306A\uFF09\u95A2\u4FC2\u3092\u3044\u3046\u3002\u968F\u4F34\u306E\u6982\u5FF5\u306F\u6570\u5B66\u306B\u904D\u5728\u3057\u3001\u6700\u9069\u5316\u3084\u52B9\u7387\u306B\u95A2\u3059\u308B\u76F4\u89B3\u7684\u6982\u5FF5\u3092\u660E\u3089\u304B\u306B\u3059\u308B\u3002 \u6700\u3082\u7C21\u6F54\u306A\u5BFE\u79F0\u7684\u5B9A\u7FA9\u306B\u304A\u3044\u3066\u3001\u570F \U0001D49E \u3068 \U0001D49F \u306E\u9593\u306E\u968F\u4F34\u3068\u306F\u3001\u4E8C\u3064\u306E\u95A2\u624B \u306E\u5BFE\u3067\u3042\u3063\u3066\u3001\u5168\u5358\u5C04\u306E\u65CF \u304C\u5909\u6570 X, Y \u306B\u95A2\u3057\u3066\u81EA\u7136\uFF08\u3042\u308B\u3044\u306F\u51FD\u624B\u7684\uFF09\u3068\u306A\u308B\u3082\u306E\u3092\u8A00\u3046\u3002\u3053\u306E\u3068\u304D\u3001\u95A2\u624B F \u3092\u5DE6\u968F\u4F34\u51FD\u624B\u3068\u547C\u3073\u3001\u4ED6\u65B9 G \u3092\u53F3\u968F\u4F34\u51FD\u624B\u3068\u547C\u3076\u3002\u307E\u305F\u3001\u300CF \u306F G \u306E\u5DE6\u968F\u4F34\u3067\u3042\u308B\u300D (\u540C\u3058\u3053\u3068\u3060\u304C\u3001\u300CG \u306F F \u306E\u53F3\u968F\u4F34\u3067\u3042\u308B\u300D)\u3068\u3044\u3046\u95A2\u4FC2\u3092 \u3068\u66F8\u304F\u3002 \u4EE5\u4E0B\u3067\u306F\u3001\u3053\u306E\u5B9A\u7FA9\u3084\u4ED6\u306E\u5B9A\u7FA9\u3092\u8A73\u7D30\u5316\u3059\u308B\u3002"@ja . "\u968F\u4F34\u95A2\u624B"@ja . "In matematica, in particolare nella teoria delle categorie, l'aggiunzione \u00E8 una possibile relazione tra due funtori. L'aggiunzione \u00E8 molto frequente in matematica. Una coppia di funtori aggiunti da C a D e da D a C \u00E8 quanto serve affinch\u00E9 le due categorie C e D siano compatibili nei loro oggetti e morfismi. Per esempio, un funtore potrebbe immergere C nella sua estensione D, e l'altro funtore potrebbe restringere nuovamente D in C. Per questo genere di relazioni, l'aggiunzione formalizza i concetti intuitivi di ottimizzazione ed efficienza. and e una famiglia di biiezioni"@it . . . . "64591"^^ . . . . . . . . . . . . . . . . . . . . . . "In matematica, in particolare nella teoria delle categorie, l'aggiunzione \u00E8 una possibile relazione tra due funtori. L'aggiunzione \u00E8 molto frequente in matematica. Una coppia di funtori aggiunti da C a D e da D a C \u00E8 quanto serve affinch\u00E9 le due categorie C e D siano compatibili nei loro oggetti e morfismi. Per esempio, un funtore potrebbe immergere C nella sua estensione D, e l'altro funtore potrebbe restringere nuovamente D in C. Per questo genere di relazioni, l'aggiunzione formalizza i concetti intuitivi di ottimizzazione ed efficienza. Nella pi\u00F9 concisa definizione simmetrica, un'aggiunzione tra due categorie C e D \u00E8 una coppia di funtori, and e una famiglia di biiezioni che \u00E8 naturale per tutte le variabili X in C e Y in D. Il funtore F \u00E8 chiamato aggiunto sinistro, mentre G \u00E8 chiamato aggiunto destro. La relazione \"F \u00E8 aggiunto sinistro a G\", o equivalentemente \"G \u00E8 aggiunto destro a F\", si denota anche con Questa e altre definizioni saranno approfondite nel seguito."@it . . . "Adjungovan\u00FD funktor"@cs . "In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of \"optimal solutions\" to certain problems (i.e., constructions of objects having a certain universal property), such as the construction of a free group on a set in algebra, or the construction of the Stone\u2013\u010Cech compactification of a topological space in topology."@en . . . "Funtores adjuntos"@es . . . . . . . . . . "\u0421\u043F\u0440\u044F\u0301\u0436\u0435\u043D\u0456 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438 \u2014 \u043F\u0430\u0440\u0430 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0456\u0432, \u0449\u043E \u043F\u0435\u0440\u0435\u0431\u0443\u0432\u0430\u044E\u0442\u044C \u0443 \u043F\u0435\u0432\u043D\u043E\u043C\u0443 \u0441\u043F\u0456\u0432\u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u0456 \u043C\u0456\u0436 \u0441\u043E\u0431\u043E\u044E. \u0421\u043F\u0440\u044F\u0436\u0435\u043D\u0456 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438 \u0447\u0430\u0441\u0442\u043E \u0437\u0443\u0441\u0442\u0440\u0456\u0447\u0430\u044E\u0442\u044C\u0441\u044F \u0432 \u0440\u0456\u0437\u043D\u043E\u043C\u0430\u043D\u0456\u0442\u043D\u0438\u0445 \u0433\u0430\u043B\u0443\u0437\u044F\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438. \u041D\u0435\u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E, \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438 F \u0456 G \u0454 \u0441\u043F\u0440\u044F\u0436\u0435\u043D\u0438\u043C\u0438, \u044F\u043A\u0449\u043E \u0432\u043E\u043D\u0438 \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u044E\u0442\u044C \u0441\u043F\u0456\u0432\u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044E . \u0422\u043E\u0434\u0456 F \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043B\u0456\u0432\u0438\u043C \u0441\u043F\u0440\u044F\u0436\u0435\u043D\u0438\u043C \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u043E\u043C, \u0430 G \u2014 \u043F\u0440\u0430\u0432\u0438\u043C."@uk . . . . . "\u0421\u043F\u0440\u044F\u0301\u0436\u0435\u043D\u0456 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438 \u2014 \u043F\u0430\u0440\u0430 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0456\u0432, \u0449\u043E \u043F\u0435\u0440\u0435\u0431\u0443\u0432\u0430\u044E\u0442\u044C \u0443 \u043F\u0435\u0432\u043D\u043E\u043C\u0443 \u0441\u043F\u0456\u0432\u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u0456 \u043C\u0456\u0436 \u0441\u043E\u0431\u043E\u044E. \u0421\u043F\u0440\u044F\u0436\u0435\u043D\u0456 \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438 \u0447\u0430\u0441\u0442\u043E \u0437\u0443\u0441\u0442\u0440\u0456\u0447\u0430\u044E\u0442\u044C\u0441\u044F \u0432 \u0440\u0456\u0437\u043D\u043E\u043C\u0430\u043D\u0456\u0442\u043D\u0438\u0445 \u0433\u0430\u043B\u0443\u0437\u044F\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438. \u041D\u0435\u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E, \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u0438 F \u0456 G \u0454 \u0441\u043F\u0440\u044F\u0436\u0435\u043D\u0438\u043C\u0438, \u044F\u043A\u0449\u043E \u0432\u043E\u043D\u0438 \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u044E\u0442\u044C \u0441\u043F\u0456\u0432\u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044E . \u0422\u043E\u0434\u0456 F \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043B\u0456\u0432\u0438\u043C \u0441\u043F\u0440\u044F\u0436\u0435\u043D\u0438\u043C \u0444\u0443\u043D\u043A\u0442\u043E\u0440\u043E\u043C, \u0430 G \u2014 \u043F\u0440\u0430\u0432\u0438\u043C."@uk . . "Adjunkce je v teorii kategori\u00ED vztah mezi dv\u011Bma funktory (a t\u00EDm i vztah mezi dv\u011Bma kategoriemi), kter\u00E9 se ozna\u010Duj\u00ED jako adjungovan\u00E9 funktory, co\u017E se zna\u010D\u00ED jako , p\u0159i\u010Dem\u017E je adjungovan\u00FD zleva ke (a naopak je adjungovan\u00FD zprava k ). M\u00E1me-li funktory a , pak je , pokud pro ka\u017Ed\u00E9 a existuje bijekce p\u0159irozen\u00E1 v obou parametrech. Existence adjungovan\u00FDch funktor\u016F mezi dv\u011Bma kategoriemi vyjad\u0159uje m\u00EDrn\u011Bj\u0161\u00ED obdobu ekvivalence t\u011Bchto kategori\u00ED. Adjungovan\u00E9 funktory mezi kategoriemi jsou zobecn\u011Bn\u00EDm Galoisovy korespondence mezi \u010D\u00E1ste\u010Dn\u011B uspo\u0159\u00E1dan\u00FDmi mno\u017Einami. V obecn\u00E9 algeb\u0159e se pou\u017E\u00EDvaj\u00ED mimo jin\u00E9 ke generov\u00E1n\u00ED voln\u00FDch objekt\u016F."@cs . . . . . . . "\u5728\u7BC4\u7587\u8AD6\u4E2D\uFF0C\u51FD\u5B50\u82E5\u6EFF\u8DB3\uFF0C\u5247\u7A31\u4E4B\u70BA\u4E00\u5C0D\u4F34\u96A8\u51FD\u5B50\uFF0C\u5176\u4E2D\u7A31\u70BA\u7684\u53F3\u4F34\u96A8\u51FD\u5B50\uFF0C\u800C\u662F\u7684\u5DE6\u4F34\u96A8\u51FD\u5B50\u3002\u4F34\u96A8\u51FD\u5B50\u5728\u7BC4\u7587\u8AD6\u4E2D\u662F\u500B\u6975\u57FA\u672C\u800C\u6709\u7528\u7684\u6982\u5FF5\u3002"@zh . . . . . . . . . . . . . . "En matem\u00E1ticas, espec\u00EDficamente en teor\u00EDa de categor\u00EDas, la adjunci\u00F3n es una relaci\u00F3n entre dos funtores que aparece frecuentemente a trav\u00E9s de las distintas ramas de las matem\u00E1ticas y que captura una noci\u00F3n intuitiva de soluci\u00F3n a un problema de optimizaci\u00F3n. Dos funtores y se dicen adjuntos entre s\u00ED, si existe una familia de biyecciones que es natural para cualesquiera e . La relaci\u00F3n de que sea adjunto a izquierda de , o, equivalentemente, que sea adjunto a derecha de , se nota como ."@es . . "Na teoria das categorias, uma adjun\u00E7\u00E3o \u00E9 uma tripla consistindo de dois functores , e uma fam\u00EDlia de isomorfismos natural em ; a condi\u00E7\u00E3o de naturalidade \u00E9 expressa por para cada , e , ou equivalentemente por para cada , e . Nesse caso, \u00E9 dito adjunto esquerdo a , e \u00E9 dito adjunto direito a , e escreve-se . Segundo Saunders Mac Lane, \"functores adjuntos s\u00E3o onipresentes\". Com efeito, v\u00E1rios conceitos da matem\u00E1tica, como grupos livres, corpo de quocientes e completa\u00E7\u00E3o de espa\u00E7os m\u00E9tricos s\u00E3o casos particulares do conceito de adjun\u00E7\u00E3o."@pt .