Template:Group-like structures

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Group-like structures. The entries say whether the property is required.
Totality* Associativity Identity Divisibility Commutativity
Semicategory No Yes No No No
Category No Yes Yes No No
Groupoid No Yes Yes Yes No
Magma Yes No No No No
Quasigroup Yes No No Yes No
Loop Yes No Yes Yes 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
*Closure, which is used in many sources, is an equivalent axiom to totality, though defined differently.

fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne