Template:Group-like structures: Difference between revisions
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Revision as of 15:40, 13 December 2022
| Totalityα | Associativity | Identity | Inverse | Commutativity | |
|---|---|---|---|---|---|
| Semigroupoid | Unneeded | Required | Unneeded | Unneeded | Unneeded |
| Small category | Unneeded | Required | Required | Unneeded | Unneeded |
| Groupoid | Unneeded | Required | Required | Required | Unneeded |
| Magma | Required | Unneeded | Unneeded | Unneeded | Unneeded |
| Quasigroup | Required | Unneeded | Unneeded | Required | Unneeded |
| Unital magma | Required | Unneeded | Required | Unneeded | Unneeded |
| Semigroup | Required | Required | Unneeded | Unneeded | Unneeded |
| Loop | Required | Unneeded | Required | Required | Unneeded |
| Monoid | Required | Required | Required | Unneeded | Unneeded |
| Group | Required | Required | Required | Required | Unneeded |
| Commutative monoid | Required | Required | Required | Unneeded | Required |
| Abelian group | Required | Required | Required | Required | Required |
| ^α The closure axiom, used by many sources and defined differently, is equivalent. | |||||
