Isocategories and Tensor Functors NollWalter 1992 <p>In this paper, I show how the concepts of an <em>isocategory</em> and the corresponding concept of an <em>isofunctor</em> can be used to improve the conceptual infrastructure of many branches of mathematics. Isofunctors that involve the isocategory LIS of all linear isomorphism of finite-dimensional linear spaces are called <em>tensor functors</em>, because they can be used to clarify most uses of the term "tensor" in the literature of mathematics and physics. Of particular importance are the <em>analytic tensor functors</em>, which can serve to be the basis for a completely coordinate-free presentation of the theory of differentiable manifold </p>