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Unifying theory

Concrete examples

In this section we list a few examples, pertaining to different mathematical fields, of application of the unifying techniques described in this section.

• Maximal ideals of commutative rings
   
  
• Theories of presheaf type
  
  
• Topos-theoretic Fraïssé's construction
   
• Stone-type dualities
   
  
• Constructive field theory
  
  
• Topos-theoretic Galois Theory
  
  
• The geometry of syntax
   
• Compactifications of topological spaces
   
  
• A duality for C*-algebras
   
  
• Different constructions of spectra
   
• Free structures
   
  
• Topos-theoretic Gödel's completeness theorem
   
  
• Descent and definability
   
  
• Priestley-type dualities

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