At the moment I am writing a chapter on groupoid spaces. In this chapter I introduce the notion of a “group space” and the notion of a “groupoid space”. Of course, most of the theory is exactly the same as for groupoid schemes, so in fact I am simply editing a copy of the chapter on groupoid schemes. What I am wondering is whether it is OK to use “groupoid space”‘ and “group space”, or if I should use the longer and perhaps more correct “algebraic groupoid space” and “algebraic group space”? Or, is it better to use “groupoid in algebraic spaces” and “group algebraic space”?
For now I’ll stick to my first choice, but if you object please leave a comment.