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Automorphisms of Ω


Let ℰ be a topos, with subobject classifier Ω. We show that automorphisms of Ω in ℰ are in 1-1 correspondence with closed boolean subtoposes of ℰ, the group operation corresponding to symmetric difference of subtoposes. This helps to explain an earlier result of D. Higgs, which implied that aut (Ω) was an elementary abelian group of exponent 2. We also use this result to give an explicit description of aut Ω when ℰ is a spatial topos or a topos of presheaves.

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Johnstone, P.T. Automorphisms of Ω. Algebra Universalis 9, 1–7 (1979).

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  • Boolean Algebra
  • Distributive Lattice
  • Full Subcategory
  • Algebra UNIV
  • Symmetric Difference