I am looking for a descriptive adjective to describe the following special property that some objects in some categories enjoy: their endomorphism monoids are groups. Of course, one way this could happen is if the ambient category is a groupoid, but in the cases I am interested in, the objects in question do receive and emit noninvertible morphisms; only their endomorphisms are invertible. For example, in the category of commutative rings, polynomial rings do not enjoy this property, but (if I'm not mistaken) fields of finite transcendence degree do.

Any suggestions on a term to use?

I am looking for a descriptive adjective to describe the following special property that some objects in some categories enjoy: their endomorphism monoids are groups. Of course, one way this could happen is if the ambient category is a groupoid, but in the cases I am interested in, the objects in question do receive and emit noninvertible morphisms; only their endomorphisms are invertible. For example, in the category of commutative rings, polynomial rings do not enjoy this property, but (if I'm not mistaken) fields of finite transcendence degree do.

Any suggestions on a term to use?