More abstractly, we can think of as the full subcategory of with groups as objects.
Since groups may be identified with one-object groupoids, it is sometimes useful to regard as a -category, namely as the full sub--category of Grpd on one-object groupoids. In this case the -morphisms between homomorphisms of groups come from “intertwiners”: inner automorphisms of the target group.
On the other hand, if we regard as a full sub--category of , the -category of pointed groups, then this is locally discrete and equivalent to the ordinary -category . This is because the only pointed intertwiner between two homomorphisms is the identity.
Precisely analogous statements hold for the category Alg of algebras.