View source for Template:Group-like structures

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|+ style="background:#cee0f2; padding:0.2em 0.4em 0.2em; text-align:center; font-size:130%; line-height:1.2em; font-weight: bold" | Group-like structures
|-
!
! [[Total function|Totality]]{{ref|Alpha|α}} 
! [[Associativity]] 
! [[Identity element|Identity]] 
! [[Quasigroup|Inverse]] 
! [[Commutativity]]
|-
! [[Semigroupoid]] 
| {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
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! [[Category (mathematics)|Small category]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Groupoid]]
| {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
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! [[Magma (algebra)|Magma]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Quasigroup]]
| {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Unital magma]]
| {{yes|Required}} || {{no|Unneeded}} ||{{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Semigroup]]
| {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}  || {{no|Unneeded}}
|-
! [[Loop (algebra)|Loop]]
| {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
<!--! [[Group (mathematics)|Group]] or [[Empty domain|Empty]]
| {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}} || {{no|Unneeded}}-->
|-
! [[Monoid]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{no|Unneeded}}
|-
! [[Group (mathematics)|Group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}}
|-
! [[Commutative monoid]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{no|Unneeded}} || {{yes|Required}}
|-
! [[Abelian group]]
| {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}} || {{yes|Required}}
|-
| colspan="6" | <small>{{note|Alpha|α}}The [[closure (mathematics)|closure]] axiom, used by many sources and defined differently, is equivalent.</small>
|}<noinclude>
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