most renowned educational institution

I would imagine that the majority of people would say Harvard or Yale if they were American but as I am from the UK I will have to go for either Oxford or Cambridge, and if forced to pick between the two then I would have to say Oxford, not that I went there, but I do know that students apply to get in from all over the world so it must have something going for it. As for mentioning a category, I don't understand what you mean by this, sorry.