Isocategories and Tensor Functors

In this paper, I show how the concepts of an isocategory and the corresponding concept of an isofunctor 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 tensor functors, 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 analytic tensor functors, which can serve to be the basis for a completely coordinate-free presentation of the theory of differentiable manifold