regular monos, epis and categories

I am a bit confused about what is or should be the correct definitions of regular monos, epis and categories. In the traditional examples from algebra there are plenty of limits and colimits around, so it doesn't much matter whether you say they're the (co)equalisers of arbitrary pairs or their (co)kernel pairs. Has anyone made use of these concepts in categories which have only the bare minimum (whatever that may be) of limits and colimits? Paul Taylor. =========================================================================