What is an ideal a zero-class of?
  We characterise, in pointed regular categories, the ideals as the zero-classes of surjective relations. Moreover, we study a variation of the "Smith is Huq" condition: two surjective left split relations commute as soon as their zero-classes commute. 
N. Martins-Ferreira, A. Montoli, A. Ursini, and T. Van der Linden
math.CT