topos
Sign in to saveAlso known as topoi, toposes, elementary topos
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.
Wikidata facts
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- discoverer or inventor
- Alexander Grothendieck
- maintained by WikiProject
- WikiProject Mathematics
- generalization of
- topological space
Sources (3)
via Wikidata · CC0
~21 min read
Encyclopedic overview
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.
Excerpted from Wikipedia’s “topos” article, available under the CC BY-SA 4.0 licence.