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group object(Q765994)

From Wikidata

analogue of the definition of a group inside an arbitrary category

internal group

Language	Label	Description	Also known as
default for all languages	No label defined
English	group object	analogue of the definition of a group inside an arbitrary category	internal group

Statements

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internal category

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category theory

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defining formula

\begin{matrix} m : G \times G \to G \\ e : 1 \to G \\ i : G \to G \\ m \circ (m \times {i d}_{G}) = m \circ ({i d}_{G} \times m) \\ m \circ ({i d}_{G} \times e) = {p r o j}_{1}^{G \times 1} \\ m \circ (e \times {i d}_{G}) = {p r o j}_{2}^{1 \times G} \\ m \circ ({i d}_{G} \times i) \circ {d i a g}_{G} = m \circ (i \times {i d}_{G}) \circ {d i a g}_{G} = e \end{matrix}

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

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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(8 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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