I’m dealing with relations on relations $\mathcal{R} \subseteq \mathcal{P}(A \times A) \times \mathcal{P}(A \times A)$ that have the following properties:

• $(R_{1}, S_{1}) \in \mathcal{R} \mathrel\wedge (R_{2}, S_{2}) \in \mathcal{R} \rightarrow (R_{1} \circ R_{2}, S_{1} \circ S_{2}) \in \mathcal{R}$

• $(\forall i \in I. (R_{i}, S_{i}) \in \mathcal{R}) \rightarrow \bigl(\bigcup_{i \in I} R_{i}, \bigcup_{i \in I} S_{i}\bigr) \in \mathcal{R}$

Is there a common name for such relations?