Table of Contents
Equivalence algebras
% Note: replace “Template” with Name_of_class in previous line
Abbreviation: EqA
Definition
A \emph{equivalence algebra} is a groupoid $\mathbf{A}=\langle A,\ldots\rangle$ of type $\langle …\rangle$ such that
$\langle A,\ldots\rangle$ is a name of class
$op_1$ is (name of property): $axiom_1$
$op_2$ is …: $\ldots$
Remark: This is a template. If you know something about this class, click on the 'Edit text of this page' link at the bottom and fill out this page.
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 $\mathbf{A}$ and $\mathbf{B}$ be … . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \ldots y)=h(x) \ldots h(y)$
Definition
An \emph{…} is a structure $\mathbf{A}=\langle A,\ldots\rangle$ of type $\langle …\rangle$ such that
$\ldots$ is …: $axiom$
$\ldots$ is …: $axiom$
Examples
Example 1:
Basic results
Properties
Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described.
Finite members
$\begin{array}{lr}
f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\
\end{array}$ $\begin{array}{lr}
f(6)= &\\ f(7)= &\\ f(8)= &\\ f(9)= &\\ f(10)= &\\
\end{array}$
Subclasses
[[...]] subvariety
[[...]] expansion
Superclasses
[[...]] supervariety
[[...]] subreduct