Abstract

In this document we describe the novel concept of generalisation of tensor. We expand the concepts expressed in previous studies by considering the generalisation of the tensor concept. We introduce the generalised index of a tensor, an index describing several types of indices of a tensor. Furthermore, we describe the connection between category theory and tensor calculus. In particular, we explore the concepts of functor tensor, or functorial tensor, tensor with categories as elements. This work opens new avenues to mathematical analysis, tensor analysis, tensor theory, and category theory.