Difference between revisions of "Template:Group-like structures"
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imported>R160K (Added a footnote explaining the equivalence of "closure" and "totality" - there have been various edits back and forth between "closure" and "totality", although I hope nobody will object to a footnote) |
imported>R160K (Footnote was not displaying properly in pages in which this infobox was used, so incorporated it into the table) |
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! [[Semicategory]] | ! [[Semicategory]] | ||
| {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} | | {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} | ||
| + | |- | ||
| + | | || colspan="5" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently.</small> | ||
|} | |} | ||
| − | |||
<noinclude> | <noinclude> | ||
Revision as of 16:38, 4 November 2012
| Group-like structures | |||||
| Totality* | Associativity | Identity | Inverses | Commutativity | |
|---|---|---|---|---|---|
| Magma | Yes | No | No | No | 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 |
| Loop | Yes | No | Yes | Yes | No |
| Quasigroup | Yes | No | No | Yes | No |
| Groupoid | No | Yes | Yes | Yes | No |
| Category | No | Yes | Yes | No | No |
| Semicategory | No | Yes | No | No | No |
| *Closure, which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently. | |||||
fr:Modèle:StructuresSemblablesGroupes ja:Template:Group-like structures pl:Szablon:Struktury grupopodobne sv:Mall:Gruppliknande strukturer zh:Template:類群結構