nLab
flat modality
Contents
Context
Modalities, Closure and Reflection
Contents
Definition
On a local topos/local (∞,1)-topos , hence with extra fully faithful right adjoint to the global section geometric morphism , is canonically induced the idempotent comonad . This modality sends for instance pointed connected objects to coefficients for flat principal ∞-connections, and may therefore be referred to as the flat modality. It is itself the left adjoint in an adjoint modality with the sharp modality . If is in addition a cohesive (∞,1)-topos then it is also the right adjoint in an adjoint modality with the shape modality .
Properties
Relation to discrete and codiscrete objects
cohesion
tangent cohesion
differential cohesion
graded differential cohesion
singular cohesion
References
See the references at local topos.
Last revised on June 14, 2016 at 17:20:37.
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