Template:Group-like structures
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| Group-like structures. The entries say whether the property is required. | |||||
| Totality* | Associativity | Identity | Divisibility | Commutativity | |
|---|---|---|---|---|---|
| Semicategory | No | Yes | No | No | No |
| Category | No | Yes | Yes | No | No |
| Groupoid | No | Yes | Yes | Yes | No |
| Magma | Yes | No | No | No | No |
| Quasigroup | Yes | No | No | Yes | No |
| Loop | Yes | No | Yes | Yes | No |
| Semigroup | Yes | Yes | No | No | No |
| Monoid | Yes | Yes | Yes | No | No |
| Group | Yes | Yes | Yes | Yes | No |
| Abelian Group | Yes | Yes | Yes | Yes | Yes |
| *Closure, which is used in many sources, is an equivalent axiom to totality, though defined differently. | |||||
fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne