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# Isocategories and Tensor Functors

journal contribution

posted on 1992-01-01, 00:00 authored 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