![[Home]](/structures.gif)
Commutative groupoidsCommutative groupoids
A commutative groupoid is a structure A = (A,·) where · is any commutative binary operation on A, i.e. x·y = y·x.
Let A and B be commutative groupoids. A morphism from A to B is a function h : A→B that is a homomorphism: h(x·y) = h(x)·h(y).
| Classtype | variety |
| Equational theory | decidable |
| Quasiequational theory | |
| First-order theory | undecidable |
| Locally finite | no |
| Residual size | unbounded |
| Congruence distributive | no |
| Congruence modular | no |
| Congruence n-permutable | no |
| Congruence regular | no |
| Congruence uniform | no |
| Congruence extension property | no |
| Definable principal congruences | no |
| Equationally definable principal congruences | no |
| Amalgamation property | yes |
| Strong amalgamation property | yes |
| Epimorphisms are surjective | yes |