In the second talk in the series regarding a Zariski topology for tangent categories, we will begin by recalling what it means for a morphism to be -monic, -smooth, or -etale in a tangent category before examining some further properties of these classes of maps. Afterwards we’ll indicate what it means for a tangent category to be “sufficiently like affine schemes” before presenting what it means to be a Zariski open in such a category. Next, we’ll describe what it means for a family of maps to be a cover and then introduce the Zariski topology. Finally we’ll give some conditions which guarantee that the Zariski topology is subcanonical, show a series of examples of such categories, and conclude by presenting the definition of what it means to be a scheme in such a tangent category. This is joint work with JS Lemay.