As a preliminary note, I have absolutely no background in category theory. The concept was very briefly introduced in an introductory topology book I was reading as motivation for the introduction of groups, and it was left with very little description. Anyway, my question is the following - when speaking of the category of topological spaces, the book described the objects as topological spaces (as expected), but it stated that the morphisms were continuous maps. Here's where I'm confused. Is it simply convenient in further studies to define the morphisms as continuous mappings, or is it necessary to do so?