group object

Summary

group object ranks in the top 2% of general entities by monthly Wikipedia readership (47 views/month).^[1]

Key Facts

• group object's subclass of is recorded as monoid object^[2].
• group object's subclass of is recorded as internal category^[3].
• group object's Freebase ID is recorded as /m/0f0pz^[4].
• group object's defining formula is recorded as \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}^[5].
• group object's studied by is recorded as category theory^[6].
• group object's studied by is recorded as group theory^[7].
• group object's BabelNet ID is recorded as 03330894n^[8].
• group object's nLab ID is recorded as group object^[9].
• group object's maintained by WikiProject is recorded as WikiProject Mathematics^[10].
• group object's Microsoft Academic ID is recorded as 158425844^[11].
• group object's Encyclopedia of Mathematics article ID is recorded as Group_object^[12].
• group object's Group Properties article ID is recorded as Group_object^[13].

Why It Matters

group object ranks in the top 2% of general entities by monthly Wikipedia readership (47 views/month).^[1] It has Wikipedia articles in 8 language editions, a strong signal of global cultural recognition.^[14] It is known by 4 alternative names across languages and contexts.^[15]