Template:Group-like structures

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Revision as of 16:46, 19 August 2013 by imported>Gemisi (Inverses are not defined in general quasigroups; there is not even an identity. But unlike a general magma, left- and right-multiplication maps are bijective)
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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 No 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 pl:Szablon:Struktury grupopodobne