Template:Group-like structures
| Total | Associative | Identity | Divisible | Commutative | |
|---|---|---|---|---|---|
| Partial magma | Unneeded | Unneeded | Unneeded | Unneeded | Unneeded |
| Semigroupoid | Unneeded | Required | Unneeded | Unneeded | Unneeded |
| Small category | Unneeded | Required | Required | Unneeded | Unneeded |
| Groupoid | Unneeded | Required | Required | Required | Unneeded |
| Magma | Required | Unneeded | Unneeded | Unneeded | Unneeded |
| Quasigroup | Required | Unneeded | Unneeded | Required | Unneeded |
| Unital magma | Required | Unneeded | Required | Unneeded | Unneeded |
| Loop | Required | Unneeded | Required | Required | Unneeded |
| Semigroup | Required | Required | Unneeded | Unneeded | Unneeded |
| Monoid | Required | Required | Required | Unneeded | Unneeded |
| Group | Required | Required | Required | Required | Unneeded |
| Abelian group | Required | Required | Required | Required | Required |