MSC:  04A05  
20L13  

44A35  Convolution  
46A22  Theorems of HahnBanach type; extension and lifting of functionals and operators [See also 46M10]  
ZDM:    
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Abstract:
We give some sufficient conditions in order that
the intersection convolution $F\ast G$ of two
relations $F$ and $G$ on a groupoid $X$ be
reflexive, transitive, symmetric, and antisymmetric.
Here, $F\ast G$ is a relation on $X$ such
that
\[
\bigl(\,F\ast G\,\bigr)(x)=\,\bigcap
\,\ \bigl\{\,F\,(u)+G\,(v)\,: \qquad x=u+v\,, \quad
F\,(u)\ne \emptyset\,, \quad G\,(v)\ne \emptyset\,\bigr\}
\]
for all $x\in X$.