### Table of Contents

## Allegories

Abbreviation: **All**

### Definition

An \emph{allegory} is an expanded category $\mathbf{M}=\langle M,\circ,\text{dom},\text{rng},\text{id},\vee,\wedge,^\smile\rangle$ such that

$\ldots$ is …: $\ldots$

$\ldots$ is …: $\ldots$

Remark: This is a template.

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 allegories. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a functor $F:A\rightarrow B$ that also preserves the new operations: $h(x \ldots y)=h(x) \ldots h(y)$

### 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

### References

%^{1)}

^{1)}%F. Lastname, \emph{Title}, Journal, \textbf{1}, 23–45 MRreview