topos
Sign in to saveIn mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion of localization. The Grothendieck topoi find applications in algebraic geometry, and more general elementary topoi are used in logic.
Article
21 sectionsContents
- Grothendieck topos (topos in geometry)
- Equivalent definitions
- Giraud's axioms
- Examples
- Category of sets and G-sets
- Topoi from ringed spaces
- Pathologies
- Geometric morphisms
- Points of topoi
- Essential geometric morphisms
- Ringed topoi
- Homotopy theory of topoi
- Elementary topoi (topoi in logic)
- Introduction
- Formal definition
- Logical functors
- Explanation
- Further examples and non-examples
- See also
- Notes
- References
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion of localization. The Grothendieck topoi find applications in algebraic geometry, and more general elementary topoi are used in logic.
The mathematical field that studies topoi is called topos theory.