Is there a name for an adjunction between two categories such that


i) the unit of the adjunction is a natural isomorphism,


ii) the counit of the adjunction is a natural isomorphism?



Name for a categorical adjunction that is a "semi-equivalence"
An adjunction for which the unit is a natural isomorphism is called a [coreflective adjunction](https://ncatlab.org/nlab/show/coreflective+subcategory). An adjunction for which the counit is a natural isomorphism is called a [reflective adjunction](https://ncatlab.org/nlab/show/reflective+subcategory).


