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dbr:Semigroup
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dbr:Semigroupoid
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Semigrupoide Semigrupoid Semigroupoid 약한 범주 نصف شبه زمرة
rdfs:comment
In mathematics, a semigroupoid (also called semicategory, naked category or precategory) is a partial algebra that satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise monoids and groupoids generalise groups. Semigroupoids have applications in the structural theory of semigroups. Formally, a semigroupoid consists of: such that the following axiom holds: * (associativity) if f : A → B, g : B → C and h : C → D then h ∘ (g ∘ f) = (h ∘ g) ∘ f. Dalam matematika, semigrupoid (disebut juga semikategori, kategori terbuka atau prakategori) adalah yang memenuhi aksioma untuk kategori kecil, kecuali kemungkinan persyaratan bahwa terdapat identitas pada setiap objek. Semigrupoid menggeneralisasi semigrup dengan cara yang sama, sebagai contoh kategori kecil menggeneralisasi monoid dan grupoid menggeneralisasi grup. Semigrupoid memiliki aplikasi dalam teori struktural semigrup. Secara formal, semigrupoid terdiri dari: sedemikian rupa maka aksioma berikut berlaku: En matemáticas, un semigrupoide es un álgebra parcial que satisface los axiomas para una categoría pequeña, excepto posiblemente por el requisito que haya una identidad para cada objeto. Los semigrupoides generalizan los semigrupos de la misma manera que las categorías pequeñas generalizan los monoides y los grupoides generalizan los grupos, y tienen usos en la teoría estructural de semigrupos. 수학에서 약한 범주(semicategory 또는 semigroupoid 또는 precategory 라고도 함)는 작은 범주(카테고리,category)에 대한 공리를 만족하는 부분 대수학이다. 단, 객체(object)에 항등원이 있어야한다는 요구 사항을 제외하고서 가능하다. 약한 범주(Semigroupoid)는 작은 범주가 모노이드(monoid)를 일반화 하거나 준군(groupoid)이 군(group)을 일반화하는 것과 같은 동일한 방식으로 반군(semigroup)을 일반화 한다. 준군(Semigroupoid)은 반군(semigroup)의 구조 이론에 응용 프로그램을 가지고 있다. 형식적으로 약한 범주는 다음으로 구성된다. 다음의 공리가 성립한다. * (결합법칙)만약 이라면, 이다.
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Dalam matematika, semigrupoid (disebut juga semikategori, kategori terbuka atau prakategori) adalah yang memenuhi aksioma untuk kategori kecil, kecuali kemungkinan persyaratan bahwa terdapat identitas pada setiap objek. Semigrupoid menggeneralisasi semigrup dengan cara yang sama, sebagai contoh kategori kecil menggeneralisasi monoid dan grupoid menggeneralisasi grup. Semigrupoid memiliki aplikasi dalam teori struktural semigrup. Secara formal, semigrupoid terdiri dari: * himpunan yang disebut sebagai objek. * untuk setiap dua objek A dan B satu himpunan Mor(A,B) disebut sebagai dari A ke B. Jika f sebagai Mor(A,B) ditulis f : A → B. * untuk setiap tiga objek A, B dan C operasi biner Mor(A,B) × Mor(B,C) → Mor(A,C) disebut komposisi morfisme. Komposisi f : A → B dan g : B → C ditulis sebagai g ∘ f atau gf (beberapa lainnya menulis sebagai fg.) sedemikian rupa maka aksioma berikut berlaku: * (asosiatif) jika f : A → B, g : B → C dan h : C → D maka h ∘ (g ∘ f) = (h ∘ g) ∘ f. 수학에서 약한 범주(semicategory 또는 semigroupoid 또는 precategory 라고도 함)는 작은 범주(카테고리,category)에 대한 공리를 만족하는 부분 대수학이다. 단, 객체(object)에 항등원이 있어야한다는 요구 사항을 제외하고서 가능하다. 약한 범주(Semigroupoid)는 작은 범주가 모노이드(monoid)를 일반화 하거나 준군(groupoid)이 군(group)을 일반화하는 것과 같은 동일한 방식으로 반군(semigroup)을 일반화 한다. 준군(Semigroupoid)은 반군(semigroup)의 구조 이론에 응용 프로그램을 가지고 있다. 형식적으로 약한 범주는 다음으로 구성된다. * 데이타의 모임, 즉 집합은 객체(object, 또는 대상)로 불린다. * 두 객체 A 와 B 에서, A로부터 B로의 사상을 집합 Mor( A , B )라고한다. 그때 만약 f 가 Mor( A , B )이면 f : A → B 라고 나타낸다. * Mor( A , B ) × Mor( B , C ) → Mor( A , C )의 임의의 3개의 객체 A , B ,C 에 대해서 사상 f : A → B 및 g : B → C의 합성은 g ∘f 또는 gf로 표시된다. (일부 수학자는 이것을 fg 로 표기한다.) 다음의 공리가 성립한다. * (결합법칙)만약 이라면, 이다. En matemáticas, un semigrupoide es un álgebra parcial que satisface los axiomas para una categoría pequeña, excepto posiblemente por el requisito que haya una identidad para cada objeto. Los semigrupoides generalizan los semigrupos de la misma manera que las categorías pequeñas generalizan los monoides y los grupoides generalizan los grupos, y tienen usos en la teoría estructural de semigrupos. In mathematics, a semigroupoid (also called semicategory, naked category or precategory) is a partial algebra that satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise monoids and groupoids generalise groups. Semigroupoids have applications in the structural theory of semigroups. Formally, a semigroupoid consists of: * a set of things called objects. * for every two objects A and B a set Mor(A,B) of things called morphisms from A to B. If f is in Mor(A,B), we write f : A → B. * for every three objects A, B and C a binary operation Mor(A,B) × Mor(B,C) → Mor(A,C) called composition of morphisms. The composition of f : A → B and g : B → C is written as g ∘ f or gf. (Some authors write it as fg.) such that the following axiom holds: * (associativity) if f : A → B, g : B → C and h : C → D then h ∘ (g ∘ f) = (h ∘ g) ∘ f.
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