I'm reading Categories for the Working Mathematician by Saunders Mac Lane. At the section 5 from chapter 1, for a fixed category, he claims that every arrow with right inverse, is epic (right cancellable). He claims also that the converse is true in the category of Sets, but fails in the category of Groups. I tried by myself to find a pair of groups and an arrow having these properties, but I cannot find them.
I also read that a given group, regarded as a category with one element, one arrow per element of the group, and the composition of arrows representing the group product, is not a concrete category. How can I prove that?
Thanks in advance. Every help would be very appreciated.