nLab
reduction modality

Context

Cohesion

cohesive topos

cohesive (∞,1)-topos

cohesive homotopy type theory

Backround

Definition

Presentation over a site

Structures in a cohesive (,1)(\infty,1)-topos

structures in a cohesive (∞,1)-topos

Structures with infinitesimal cohesion

infinitesimal cohesion?

Models

Modalities, Closure and Reflection

Contents

Idea

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.

Definition

A context of differential cohesion is determined by the existence of an adjoint triple of modalities

Redʃ inf inf, Red \dashv ʃ_{inf} \dashv \flat_{inf} \,,

where RedRed and inf\flat_{inf} are idempotent comonads and ʃ infʃ_{inf} is an idempotent monad.

Here RedRed is the reduction modality. The reflective subcategory that it defines is that of reduced objects.

cohesion

tangent cohesion

differential cohesion

Revised on November 4, 2013 22:01:37 by Urs Schreiber (82.169.114.243)