## Isocategories and Tensor Functors

journal contribution

posted on 01.01.1992, 00:00 by Walter NollIn 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