Difference between revisions of "Template:Group-like structures"
Jump to navigation
Jump to search
(adding Commutative monoid) |
imported>Funandtrvl (refine category) |
||
| Line 49: | Line 49: | ||
|- | |- | ||
| colspan="6" | <small>{{note|Alpha|α}}[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.</small> | | colspan="6" | <small>{{note|Alpha|α}}[[Closure (mathematics)|Closure]], which is used in many sources, is an equivalent axiom to totality, though defined differently.</small> | ||
| − | |} | + | |}<noinclude> |
| − | <noinclude> | + | <!-- Categories below this line; interwikis at Wikidata --> |
| − | + | [[Category:Mathematics sidebar templates]] | |
| − | [[Category:Mathematics templates | ||
| − | |||
| − | |||
| − | |||
</noinclude> | </noinclude> | ||
Latest revision as of 21:08, 28 July 2020
| Group-like structures | |||||
|---|---|---|---|---|---|
| Totalityα | Associativity | Identity | Invertibility | 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 |
| Loop | Required | Unneeded | Required | Required | Unneeded |
| Semigroup | Required | Required | Unneeded | Unneeded | Unneeded |
| Inverse Semigroup | Required | Required | Unneeded | Required | Unneeded |
| Monoid | Required | Required | Required | Unneeded | Unneeded |
| Commutative monoid | Required | Required | Required | Unneeded | Required |
| Group | Required | Required | Required | Required | Unneeded |
| Abelian group | Required | Required | Required | Required | Required |
| ^α Closure, which is used in many sources, is an equivalent axiom to totality, though defined differently. | |||||