Template:Group-like structures: Difference between revisions
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m Add a footnote because the term "groupoid" can be confusing |
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! [[Magma (algebra)|Magma]] |
! [[Magma (algebra)|Magma]] |
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! [[Category (mathematics)|Category]] |
! [[Category (mathematics)|Category]] |
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! <sup>1</sup><small>Also called groupoids</small> |
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Revision as of 04:20, 18 September 2010
| Group-like structures | ||||
| Totality | Associativity | Identity | Inverses | |
|---|---|---|---|---|
| Group | Yes | Yes | Yes | Yes |
| Monoid | Yes | Yes | Yes | No |
| Semigroup | Yes | Yes | No | No |
| Loop | Yes | No | Yes | Yes |
| Quasigroup | Yes | No | No | Yes |
| Magma | Yes | No | No | No |
| Groupoid | No | Yes | Yes | Yes |
| Category | No | Yes | Yes | No |