nLab
(infinity,1)-geometric morphism

Context

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Idea

By categorification of the notion of geometric morphism, an (,1)(\infty,1)-geometric morphism is a pair of adjoint (∞,1)-functors between (∞,1)-toposes where the leftadjoint is left-exact.

Definition

For H\mathbf{H} and K\mathbf{K} two (∞,1)-toposes, a (,1)(\infty,1)-geometric morphism f:HKf : \mathbf{H} \to \mathbf{K} is

The (non-full) sub-(∞,1)-category of (∞,1)Cat on (∞,1)-toposes and (,1)(\infty,1)-geometric morphisms between them is (∞,1)Toposes.

Further details

For the moment see the discussion and the further links at geometric morphism

References

section 6.3.1 in

Revised on November 3, 2011 14:35:50 by Stephan (79.227.171.249)