Modalities, Closure and Reflection
In a context of synthetic differential geometry/differential cohesion the reduction modality characterizes reduced objects. It forms itself the left adjoint in an adjoint modality with the infinitesimal shape modality.
A context of differential cohesion is determined by the existence of an adjoint triple of modalities
where and are idempotent comonads and is an idempotent monad.
Here is the reduction modality. The reflective subcategory that it defines is that of reduced objects.
graded differential cohesion