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It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.

Morphisms

Let A and B be ... . A morphism from A to B is a function h : A→B that is a homomorphism: h(x ... y) = h(x) ... h(y).

Definition

An ... is a structure A = (A,...) of type (...) such that

... is ...: axiom, and
... is ...: axiom.

Some results

Examples

Feel free to add or delete properties from this list. The present list may contain properties that are not relevant to the class that is being described.

Properties

Classtype
Equational theory
Quasiequational theory
First-order theory
Locally finite
Residual size
Congruence distributive
Congruence modular
Congruence n-permutable
Congruence regular
Congruence uniform
Congruence extension property
Definable principal congruences
Equationally definable principal congruences
Amalgamation property
Strong amalgamation property
Epimorphisms are surjective

Finite members

[Size 1]?: 1
[Size 2]?:
[Size 3]?:
[Size 4]?:
[Size 5]?:
[Size 6]?:

Subclasses

...? subvariety
...? expansion

Superclasses

...? supervariety
...? subreduct