### Table of Contents

## Reflexive relations

Abbreviation: **RefRel**

### Definition

A \emph{reflexive relation} is a structure $\mathbf{X}=\langle X,R\rangle$ such that $R$ is a \emph{binary relation on $X$} (i.e. $R\subseteq X\times X$) that is

reflexive: $xRx$

##### Morphisms

Let $\mathbf{X}$ and $\mathbf{Y}$ be reflexive relations. A morphism from $\mathbf{X}$ to $\mathbf{Y}$ is a function $h:A\rightarrow B$ that is a homomorphism: $xR^{\mathbf X} y\Longrightarrow h(x)R^{\mathbf Y}h(y)$

### Definition

### 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

### Superclasses

Directed graphs supervariety