(Q765994)

English

group object

analogue of the definition of a group inside an arbitrary category

In more languages

Statements

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internal category

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category theory

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defining formula

{\begin{aligned}&m\colon G\times G\to G\\&e\colon 1\to G\\&i\colon G\to G\\&m\circ (m\times \mathrm {id} _{G})=m\circ (\mathrm {id} _{G}\times m)\\&m\circ (\mathrm {id} _{G}\times e)=\mathrm {proj} _{1}^{G\times 1}\\&m\circ (e\times \mathrm {id} _{G})=\mathrm {proj} _{2}^{1\times G}\\&m\circ (\mathrm {id} _{G}\times i)\circ \mathrm {diag} _{G}=m\circ (i\times \mathrm {id} _{G})\circ \mathrm {diag} _{G}=e\end{aligned}}

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

1 reference

Encyclopedia of Mathematics article ID

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1 reference

Freebase Data Dumps

publication date

28 October 2013

Group Properties article ID

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Microsoft Academic ID

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Sitelinks

Wikipedia(7 entries)

Wikibooks(0 entries)

Wikinews(0 entries)

Wikiquote(0 entries)

Wikisource(0 entries)

Wikiversity(0 entries)

Wikivoyage(0 entries)

Wiktionary(0 entries)

Multilingual sites(0 entries)

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