Tangent mappings and convergent sequences in the Lipschitz category

The standard definition of a derivative in linear spaces is extended to a definition of tangency in the Lipschitz category, without any assumed algebraic structure on the underlying spaces.  Tangency is characterized topologically, that is, solely in terms of continuity, without using any algebraic concepts or other analytical concepts. The mappings in the Lipschitz category are characterized as the class of functions that preserve topologically convergent sequences of finite variation.