Difference between revisions of "Template:Group-like structures"
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imported>Cuihtlauac |
imported>INLegred (Changed Category to Small Category, a Category is not in general an Algebraic structure by the definitions listed on Wikipedia because the objects do not form a set.) |
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| {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} | | {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} | ||
|- | |- | ||
| − | ! [[Category (mathematics)|Category]] | + | ! [[Small Category (mathematics)|Category]] |
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} | | {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} | ||
|- | |- | ||
Revision as of 16:02, 12 December 2018
| Group-like structures | |||||
|---|---|---|---|---|---|
| Totalityα | Associativity | Identity | Invertibility | Commutativity | |
| Semigroupoid | Unneeded | Required | Unneeded | Unneeded | Unneeded |
| Category | Unneeded | Required | Required | Unneeded | Unneeded |
| Groupoid | Unneeded | Required | Required | Required | Unneeded |
| Magma | Required | Unneeded | Unneeded | Unneeded | Unneeded |
| Quasigroup | Required | Unneeded | Unneeded | Required | 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 |
| 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