(0,1)-topos in nLab

Contents

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

• J. C. Baez, M. Shulman, Lectures on n-categories and cohomology , pp.1-68 in J. C. Baez, P. May (eds.), Towards Higher Categories, Springer Heidelberg 2010. (preprint; section 5.3)

• Jacob Lurie, Higher Topos Theory , Princeton UP 2009. (section 6.4.2)

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