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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorTim Campion
   • CommentTimeFeb 23rd 2021
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   Author: Tim Campion
   Format: MarkdownItexAdded a "warning" for something that tripped me up: the classifying topos of a classical first-order theory is typically _not_ Boolean, even though the classifying pretopos _is_ Boolean. For a topos to be Boolean is much stronger -- as Blass and Scedrov showed, it implies $\aleph_0$-categoricity. <a href="https://ncatlab.org/nlab/revision/diff/Boolean+topos/31">diff</a>, <a href="https://ncatlab.org/nlab/revision/Boolean+topos/31">v31</a>, <a href="https://ncatlab.org/nlab/show/Boolean+topos">current</a>

   Added a “warning” for something that tripped me up: the classifying topos of a classical first-order theory is typically not Boolean, even though the classifying pretopos is Boolean. For a topos to be Boolean is much stronger – as Blass and Scedrov showed, it implies $\aleph_0$-categoricity.

   diff, v31, current

2. • CommentRowNumber2.
   • CommentAuthorGuest
   • CommentTimeOct 15th 2022
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   Author: Guest
   Format: MarkdownItexThis article states that > Every cartesian closed Boolean pretopos is in fact a topos. Is every [[cartesian closed]] [[Boolean category]] a topos as well?

   This article states that

   Every cartesian closed Boolean pretopos is in fact a topos.

   Is every cartesian closed Boolean category a topos as well?