Difference between revisions of "Template:Group-like structures"
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! [[Monoid]] | ! [[Monoid]] | ||
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} | | {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} | ||
| + | |- | ||
| + | ! [[Commutative monoid]] | ||
| + | | {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} | ||
|- | |- | ||
! [[Group (mathematics)|Group]] | ! [[Group (mathematics)|Group]] | ||
Revision as of 04:49, 20 December 2019
| 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. | |||||
fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne