Artin glueings of toposes as adjoint split extensions

Artin glueings of frames correspond to adjoint split extensions in the category and finite-meet-preserving maps. We extend these ideas setting toposes show that a 2-categorical notion 2-category toposes, finite-limit-preserving functors natural transformations. A morphism between is introduced, which allows Ext(H,N) be constructed. contravariantly equivalent Hom(H,N), moreover, this can extended 2-natural contravariant equivalence Hom 2-functor naturally defined Ext 2-functor.