Template:Group-like structures

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Revision as of 16:40, 4 November 2012 by imported>R160K (Changed the colspan of "Group-like structures" from 5 to 6 so that it stretch over the "Commutativity" column as well)
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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.

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