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Reflexive relations
Abbreviation: RefRel
Definition
A reflexive relation is a structure $\mathbf{X}=\langle X,R\rangle$ such that $R$ is a binary relation on $X$ (i.e. $R\subseteq X\times X$) that is
reflexive: $xRx$
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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 $\mathbf{X}$ 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
References
Trace: » reflexive_relations