nLab
coreduced object
Redirected from "coreduced objects".
Contents
Context
Cohesion
Discrete and concrete objects
Modalities, Closure and Reflection
Contents
Idea
In a context of synthetic differential geometry/differential cohesion a coreduced object is one all whose infinitesimal paths are constant. Compare the discrete objects, in which all paths are constant, meaning all discrete objects are also coreduced.
Definition
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.
A coreduced object or coreduced type is one in the full subcategory defined by the infinitesimal shape modality or equivalently the infinitesimal flat modality .
Note that an object being coreduced is the same as it being formally etale.
Examples
cohesion
infinitesimal cohesion
tangent cohesion
differential cohesion
graded differential cohesion
singular cohesion
Last revised on August 29, 2017 at 16:19:24.
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