nLab
(0,1)-topos
Context
$(0,1)$ -Category theory
(0,1)-category theory : logic , order theory

(0,1)-category

proset , partially ordered set (directed set , total order , linear order )

lattice , semilattice

lattice of subobjects

complete lattice , algebraic lattice

distributive lattice , completely distributive lattice , canonical extension

hyperdoctrine

(0,1)-topos

Heyting algebra

frame , locale

Theorems Stone duality

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Topos Theory
topos theory

Background Toposes Internal Logic Topos morphisms Cohomology and homotopy In higher category theory Theorems
Contents
Idea
The notion of $(0,1)$ -topos is that of topos in the context of (0,1)-category theory .

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

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

References
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Last revised on October 1, 2016 at 08:54:05.
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