The (2,1)-category is the 2-category whose
2-morphisms are natural transformations, which are necessarily natural isomorphisms.
This is the full sub-2-category of Cat on those categories that are groupoids.
One may regard also just as a 1-category by ignoring the natural isomorphisms between functors. This 1-category may be equipped with the natural model structure on groupoids to provide a 1-categorical presentation of the full -category.