## 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: $xR^{\mathbf X} y\Longrightarrow h(x)R^{\mathbf Y}h(y)$

Example 1:

### 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.

Classtype variety decidable yes no no

### Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ \end{array}$ $\begin{array}{lr} f(6)= &\\ f(7)= &\\ f(8)= &\\ f(9)= &\\ f(10)= &\\ \end{array}$

### Superclasses

Directed graphs supervariety