## Toposes, triples, and theories |

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Abelian groups Adjoint Functor algebra structure bijection Boolean topos category of models category of sheaves codomain coequalizer colimits composite construction contractible coequalizer Corollary corresponding cotriple countable defined definition denote dense diagram commutes disjoint embedding equalizer equivalence relation exact functor example Exercise fact finite limits following diagram FP-theory Freyd's full subcategory function functor category functor F geometric morphism given global element global section graph Grothendieck topology hence Heyting algebra Hom(C homomorphism identity implies inclusion induced map inverse image kernel pair left adjoint monic mono monoid monomorphism natural isomorphism natural transformation notation open set opfibration parallel pair preserves finite presheaf Proof Proposition prove pullback quotient reflects isomorphisms reflexive regular epi regular epimorphic representable functors right adjoint Section 1.7 sheaf Show sieve sketch square subobject subset sums Suppose surjective terminal object Theorem theory topological space toposes triple tripleable underlying functor universal element Yoneda Lemma