nLab
affine modality

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Higher geometry

Contents

Idea

Given a suitable line object 𝔸 1\mathbb{A}^1 in a suitable ambient (∞,1)-topos, then there exists the cohomology localization at morphisms that induces equivalences in cohomology with coefficients in 𝔸 1\mathbb{A}^1.

In this case the right adjoint to the reflector typically has the interpretation of producing spaces which are “affine” in that they are entirely characterized by their function ∞-algebra? with coefficients in 𝔸 1\mathbb{A}^1.

Therefore in this case the localization modality deserves to be called the affine modality.

Examples

Examples for this in higher algebraic geometry and synthetic differential geometry are discussed at function algebras on ∞-stacks? in the section Localization of the (∞,1)-topos at R-cohomology.

Last revised on November 4, 2013 at 22:30:24. See the history of this page for a list of all contributions to it.