  We describe dual notions of tangent bundle for an infinity-topos, each
underlying a tangent infinity-category in the sense of Bauer, Burke and the
author. One of those notions is Lurie's tangent bundle functor for presentable
infinity-categories, and the other is its adjoint. We calculate that adjoint
for injective infinity-toposes, where it is given by applying Lurie's tangent
bundle on infinity-categories of points.
