Template:Group-like structures
Revision as of 15:39, 20 September 2012 by imported>Quondum (Moving badly placed line break in caption)
| Requirements of group-like structures | |||||
| Totality | Identity | Associativity | Inverses | Commutativity | |
|---|---|---|---|---|---|
| Magma | Yes | No | No | No | No |
| Unital | Yes | Yes | No | No | No |
| Quasigroup | Yes | No | No | Yes | No |
| Loop | Yes | Yes | No | Yes | No |
| Semigroup | Yes | No | Yes | No | No |
| Monoid | Yes | Yes | Yes | No | No |
| Group | Yes | Yes | Yes | Yes | No |
| Abelian Group | Yes | Yes | Yes | Yes | Yes |
| Groupoid | No | Yes | Yes | Yes | No |
| Category | No | Yes | Yes | No | No |
| Semicategory | No | No | Yes | No | No |
| Note: A quasigroup with associativity (equivalently, a semigroup with inverses) already has an identity element, and is therefore a group. | |||||
af:Sjabloon:Groepagtige strukture cs:Šablona:Grupové struktury fr:Modèle:StructuresSemblablesGroupes ja:Template:Group-like structures pl:Szablon:Struktury grupopodobne sv:Mall:Gruppliknande strukturer zh:Template:類群結構