A new characterisation of groups amongst monoids
  We prove that a monoid $M$ is a group if and only if, in the category of monoids, all points over $M$ are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo and Van der Linden which characterises groups amongst monoids as the protomodular objects. 
Xabier Garc\'ia-Mart\'inez
math.CT