group object (Q765994)
analogue of the definition of a group inside an arbitrary category
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Current Data About group object
(P279) (Q2785361)
(Q6047782)
(P2534) \begin{aligned}&m\colon G\times G\to G\\&e\colon1\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\times1}\\&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}
(P2579) (Q217413)
(P6104) (Q8487137)
other details
description analogue of the definition of a group inside an arbitrary category

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