# Is the 2-Category of Groupoids Locally Presentable?

I am wondering if the 2-Category of groupoids is Locally Presentable? Locally presentable means the category is accessible and co-complete.

Edit: It has been pointed out that the category of Groupoids is Locally Preseantable. It would be useful if I could find a theorem that says that if your base category, namely groupoids, was LP, then so is the 2-category on that base. I have done a bit of research and I cannot find anything to that effect. I still cannot say if the 2-category of Groupoids is LP.

• The $1$-category of groupoids is the category of models of a limit sketch, so it is locally presentable, but what does it mean for a $2$-category to be locally presentable? – Arnaud D. Jul 24 at 5:51
• @ArnaudD. Hi, so I am really not sure. Are you suggesting that there is no sense in which a 2-category can be locally presentable? – Ben Sprott Jul 24 at 13:54
• @ArnaudD. I am now a little sure that a 2 category can be LP. Is it the case that the 2 cat is LP if the underlying cat is LP: ie, since groupoids is LP the 2-cat of groupoids is LP? – Ben Sprott Jul 24 at 14:31