I am wondering if the 2-сategory of groupoids is locally presentable. Locally presentable means the category is accessible and co-complete.


It has been pointed out that the category of groupoids is locally presentable. 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.



Is the 2-сategory of groupoids locally presentable?
This is true. 


Since the $2$-category of groupoids is equivalent to the $2$-category of $1$-truncated spaces, the statement follows immediately from 5.5.1.8 and 5.5.6.21 in Lurie's Higher Topos Theory. 


