nLab
(0,1)-topos

Context

(0,1)(0,1)-Category theory

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Contents

Idea

The notion of (0,1)(0,1)-topos is that of topos in the context of (0,1)-category theory.

The notion of (0,1)(0,1)-topos is essentially equivalent to that of Heyting algebra; similarly, a Grothendieck (0,1)(0,1)-topos is a locale.

Notice that every (1,1)(1,1)-Grothendieck topos comes from a localic groupoid, i.e. a groupoid internal to locales, hence a groupoid internal to (0,1)(0,1)-toposes. See classifying topos of a localic groupoid for more.

References

section 6.4.2 of

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Revised on November 27, 2012 11:01:19 by Urs Schreiber (82.169.65.155)