nLab
sharp modality

Contents

Definition

On a local topos/local (∞,1)-topos H\mathbf{H}, hence equipped with a fully faithful extra right adjoint coDisccoDisc to the global section geometric morphism (DiscΓ)(Disc \dashv \Gamma), is induced an idempotent monad coDiscΓ\sharp \coloneqq coDisc \circ \Gamma, a modality which we call the sharp modality. This is itself the right adjoint in an adjoint modality with the flat modality DiscΓ\flat \coloneqq Disc \circ \Gamma.

Properties

Relation to discrete and codiscrete objects

cohesion

differential cohesion

References

See the references at local topos.

Revised on January 4, 2014 03:03:13 by David Corfield (87.114.17.155)