About: Pushout (category theory)

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Pushout (category theory) Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/3x6UdaG3Mg

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain. The pushout consists of an object P along with two morphisms X → P and Y → P that complete a commutative square with the two given morphisms f and g. In fact, the defining universal property of the pushout (given below) essentially says that the pushout is the "most general" way to complete this commutative square. Common notations for the pushout are and .

Attributes	Values
rdfs:label	Pushout (de) Somme amalgamée (fr) 밂 (범주론) (ko) Pushout (category theory) (en) Кодекартов квадрат (ru) 推出 (范畴论) (zh) Розшарований кодобуток (uk)
rdfs:comment	Das Pushout (auch Kofaserprodukt, kokartesisches Quadrat, Fasersumme, amalgamierte Summe) ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie. Es handelt sich um die zum Pullback duale Konstruktion. (de) 범주론에서 밂(영어: pushout 푸시아웃[*])은 어떤 한 쌍의 사상에 의해 결정되는, 쌍대곱의 일반화이다. 일부 범주에서는 흔히 올쌍대곱(영어: fibered coproduct)이라고 불린다. (ko) Кодекартов квадрат (также — универсальный квадрат) — теоретико-категорное понятие, двойственное понятию декартова квадрата. Кодекартов квадрат является частным случаем копредела. (ru) Розшарований кодобуток (також розшарована сума, амальгама) — поняття в теорії категорій, двоїсте поняттю розшарованого добутку. Розшарований кодобуток єкограницею діаграми, що складається із двох морфізмів f: Z → X, g: Z → Y. Він складається з об'єкта P і двох морфізмів X → P і Y → P, що разом із початковими морфізмами утворюють діаграму, що називається кодекартовим квадратом. (uk) 在范畴论中，一个数学领域，推出（也称为纤维餘积、纤维和、共合和或餘笛卡尔方块）是由具有公共定义域的两个态射 f : Z → X 与 g : Z → Y 组成的的餘极限。推出是拉回的。 (zh) In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain. The pushout consists of an object P along with two morphisms X → P and Y → P that complete a commutative square with the two given morphisms f and g. In fact, the defining universal property of the pushout (given below) essentially says that the pushout is the "most general" way to complete this commutative square. Common notations for the pushout are and . (en) En mathématiques, la somme amalgamée est une opération entre deux ensembles constituant les espaces d'arrivée de deux applications définies sur un même troisième ensemble. Le résultat satisfait une propriété universelle de factorisation de diagrammes, duale de celle du produit fibré et qui peut être valable dans d'autres catégories que celle des ensembles, comme celle des groupes. Dans la catégorie des espaces topologiques, la somme amalgamée intervient ainsi dans la description de certains espaces, dont le groupe fondamental se calcule alors à l'aide du théorème de van Kampen. (fr)
foaf:depiction
dct:subject	Limits (category theory)
Wikipage page ID	582024 (xsd:integer)
Wikipage revision ID	1079080398 (xsd:integer)
Link from a Wikipage to another Wikipage	Pullback (category theory) Ronald Brown (mathematician) Algebraic topology Homomorphism Inclusion map Commutative rings Mathematics Quotient group Free product with amalgamation Full subcategory Modulo (jargon) Monoid Morphism Connected space Coproduct Closure (mathematics) Commutative diagram Fundamental group Span (category theory) Subgroup Wedge sum Adjunction space Domain of a function Dual (category theory) Pointed space Equivalence relation Diagram (category theory) Isomorphism Ring (mathematics) Group (mathematics) Intersection (set theory) Covering space Tensor product Abelian category Abelian group Least common multiple Limits (category theory) Coequalizer Cokernel Disjoint union Free product Free product of associative algebras Groupoid Initial object Integer Category (mathematics) Category of abelian groups Category of groups Category of modules Category of rings Category of topological spaces Category theory Seifert–van Kampen theorem Set (mathematics) Union (set theory) Disjoint union topology Subspace topology Universal property Subset Ring homomorphism Preimage J.P. May Simply connected Direct sum of abelian groups Colimit Object (category theory) Zero group
Link from a Wikipage to an external page	http://groupoids.org.uk/topgpds.html http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html http://ncatlab.org/nlab/show/pushout
sameAs	Pushout (category theory) Pushout (category theory) Pushout (category theory) Pushout (category theory) Pushout (category theory) Pushout (category theory) Pushout (category theory) Pushout (category theory) Pushout (category theory)

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3332 as of Dec 5 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 52 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software